If y = 1 1/x 1/x 2 1/x 3 ∞ with x>1, then dy/dx is equal to If y = 2 log x , then dy/dx is equal to If y = 4x – 5 is tangent to the curve y 2 = px 3 q at (2, 3), thenY=log (x2/e2) diff wr to x , we get dy/dx=1/ (x2/e2) (2x/e2) =2/x diff wr to x again d2y/dx2=2/x2 Thanks & RegardsGet an answer for '`y = x^(2/x)` Use logarithmic differentiation to find dy/dx' and find homework help for other Math questions at eNotes
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Taking logarithm of both sides, we get log y = `log (1 1/"x")^"x"` ∴ log y = x `log (1 1/"x")` Differentiating both sides wrtx, we get `1/"y" * "dy"/"dx" = "x" * "d"/"dx" log (1 1/"x") log (1 1/"x") * "d"/"dx" ("x")`Y = logx x2 a2 y1 = dxdy = x x2 a2 1 (1 2 x2 a2 2x )y1 = x x2 a2 1 ( x2 a2 x2 a2 x )⇒ y1 ( x2 a2 ) =1Again differentiate,⇒ y2 ( x2 a2 ) 2 x2 a2 12xy1 = 0⇒ y2 (x2 a2)xy1 = 0Answer to Solve the initial value problem dy/dx = (y^2 1)/(x^2 1), y(2) = 2 By signing up, you'll get thousands of stepbystep solutions to
Ex 96, 7 For each of the differential equation given in Exercises 1 to 12, find the general solution 𝑥𝑙𝑜𝑔𝑥 𝑑𝑦/𝑑𝑥𝑦=2/𝑥 𝑙𝑜𝑔𝑥 Step 1 Put in form 𝑑𝑦/𝑑𝑥 Py = Q xlog x 𝑑𝑦/𝑑𝑥 y = 2/𝑥 log x Dividing by x log x, 𝑑𝑦/𝑑𝑥𝑦" × " 1/(𝑥 log𝑥 ) = 2/𝑥 𝑙𝑜𝑔 𝑥" × " 1/(𝑥 log𝑥 ) 𝑑𝑦/𝑑𝑥 If x = sin(\(\frac{1}{a}\)log y) , show that (1–x2)y2–xy1–a2 y = 0 Note y 2 represents second order derivative ie \(\frac{d^2y}{dx^2}\) and y 1 = dy/dx Given, x = sin(\(\frac{1}{a}\) log y) \((logy)=asin^{1}x\) y = \(e^{asin^{1}x}\)equation 1 to prove (1 x 2)y 2xy 1 a 2 =0 We notice a second–order derivative in the expression to be proved so first take the step to Delta2 said No it doesn't matter where you put the constant neither if you set it equal to or , because given an initial condition you will get the same formula for v in both cases, but the exact value of the constants will be different (for example if you find k=2 for the one case, you ll find k=1/2 for the other case) nice delta Jul 1
Compute $$\iiint\frac{xz}{1x^2y^2}\,dz\,dy\,dx,$$ where $1≤x^2y^2≤3, 0≤z≤3$ I've tried it But I'm only confused with $\theta$ I think it should be $0$ to $2\pi$, but that'll make the whole value zero We have to solve this by the cylindrical method Without solving for theta I get $\frac{9}{2{(π/6)4}}$ As log(xy)=x^2y^2 or logxlogy=x^2y^2 assuming base is e, we have on differentiation 1/x1/y(dy)/(dx)=2x2y(dy)/(dx) or (dy)/(dx)(2y1/y)=1/x2x or (dy)/(dx)=(1/x2x)/(2y1/y)=(y2x^2y)/(2xy^2x) In case base is 10, we can write it as lnx/ln10lny/ln10=x^2y^2 and differentiating gives us 1/ln10(1/x1/y(dy)/(dx))=2x2y(dy)/(dx) or (dy)/(dx)(2yln101/y)=2xln101/x or (dy)/(dx)=(2xln101/x)/(2yln101/y)=(y2x^2yln10)/(2xy^2ln10x)Y = log(x 1/x) y = log((x^21)/x) y = log(x^21) log x Now, you have to recall the derivative formula for logarithmThat is, log y = 1/y * dy
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Answer to Find dy/dx for the following y = (1 x)/(1 x) By signing up, you'll get thousands of stepbystep solutions to your homework If y = e a cos1 x , 1 Derivative of y = ln u (where u is a function of x) Unfortunately, we can only use the logarithm laws to help us in a limited number of logarithm differentiation question types Most often, we need to find the derivative of a logarithm of some function of xFor example, we may need to find the derivative of y = 2 ln (3x 2 − 1) We need the following formula to solve such problems
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Answer to dy 24(2 5)2 dy O Find da , where da ( 3) (ac 5) 3 dy (ac 5) 2 O y dx (x 3)2 (a 3)3 dy 24(x 5)2 O dx (2 3) 4 dy 1 O dx (x 3)6 8 The given differential equation is solved using the following steps (i) Take natural logaritm on both sides and then simplify the obtained equation using the properties of logaritm I was going through past papers of ODEs course I came across a question solve $$\frac{dy}{dx} = \frac{1}{xy^2},\qquad y(2) = 0$$ I have no clue how to proceed I have suspicion that this equation has no closed form solution and may be there was a mistake in the question Course is a basic course on ODEsGet 11 help now from expert Calculus tutors Solve it with our calculus problem solver and calculator COMPANY About Chegg
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Y = log {x√ (1x)} dy/dx = 1/ {x√ (1x^2)} 1 {1/2√ (1x^2)}2x dy/dx = 1/ {x√ (1x^2)} 1 x/√ (1x^2) dy/dx = 1/ {x√ (1x^2)} {√ (1x^2) x }/√ (1x^2) dy/dx = 1/√ (1x^2) , Answer 13K viewsBernoulli's equation has form, \frac{dy}{dx}p(x)y=q(x)y^n Now, consider this, \frac{dz}{dx}z^2x=z^2z This easily simplifies to, \frac{dz}{dx}z=(1x^2)z^2 where p(x)=1 Bernoulli's equation has form, d x d y p ( x ) y = q ( x ) y n Now, consider this, d x d z z 2 x = z 2 z This easily simplifies to, d x d z − z = ( 1 − x 2 ) z 2 where p ( x ) = − 1Click here👆to get an answer to your question ️ If y = log7 (log x) find dydx Join / Login >> Class 12 >> Maths >> Continuity and Differentiability >> Derivative of Exponential and Logarithmic Functions Let y = e x 1 then find d x 2 d 2 y
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If ∫ a 0 x 2 − 1 1 − x d x = − 1 2, then the value of a is equal to 2 If x denotes the greatest integer less than or equal to x, then the value of ∫ 0 2 ( x − 2 x) d x is equal to 3 The differential equation representing the family of curves y 2 = 2 c ( x 3 c), where c is a positive parameter, is ofFind dy/dx y^2=1/(1x^2) Differentiate both sides of the equation Differentiate the left side of the equation Tap for more steps Differentiate using the chain rule, which states that is where and Tap for more steps To apply the Chain Rule, set asIf 2x 2 3xy y 2 x 2y 8 = 0, then dy/dx is equal to If 3 ≤ 3t 18 ≤ 18, then which one of the following is correct?
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Question (1 point) Find dy when dr log(2) y = 1 log(x) = = (1 point) Use logarithmic differentiation to find the derivative y = x2 1 x2 2 y' = This question hasn't been solved yet Ask an expert Ask an expert Ask an expert done loading Show transcribed image text Expert AnswerTill infinite Find dy/dx Please give the solutionWrite in the form y=x^y since x^x^x^x is till infinite, we can consider it to be y, then take l Book a Trial With Our Experts × Given, We have to find the derivative of y Differentiating y with respect to x, Derivative of log x is 1/x Using Chain Rule of Differentiation, rosariomividaa3 and 13 more users found this answer helpful heart outlined Thanks 9 star
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Weekly Subscription $199 USD per week until cancelled Monthly Subscription $699 USD per month until cancelled Annual Subscription $2999 USD per year until cancelledLog y = log (x1)log (x2) 1/2log x 1/ydy/dx = 1/ (x1) 1/ (x2) 1/2x dy/dx= y 2x (x2)2x (x1) (x1) (x2)/2x (x1) (x2) dy/dx = { (x1) (x2)/√x} 2x^2–4x2x^2–2xx^23x2/2x (x1) (x2) dy/dx = (3x^2–3x2)/2x√x Answer 3K views · Find an answer to your question if ylogx = xy , prove thatdy/dx = logx/(1 logx)^2
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If 3 By 2 Plus I Root3 By 2 Power 50 Equal 3 25 X Iy Where X And Y Are Real Then The Ordered Pair X Y Is If 3 sin (xy) 4 cos (xy) = 5, then dy/dx = If 3 Tan Theta Tan Phi Is 1Suppose a dependent variable y represents a function f of an independent variable x, that is, = () Then the derivative of the function f, in Leibniz's notation for differentiation, can be written as (())The Leibniz expression, also, at times, written dy/dx, is one of several notations used for derivatives and derived functionsA common alternative is Lagrange's notationLet's simplify it First dy/dx = (y/x 1)/(y/x 1) Taking y = vx dy/dx = v xdv/dx Therefore, dx/x = (v 1)dv / (v^2 1) Integrating we get log (1/x) logc = arctan (y/x) 1/2 log
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Manbar Singh, Meritnation Expert added an answer, on Manbar Singh answered this We have, y = log x cos x x 2 1 x 2 1 Let y = u v where u = log x cos x and v = x 2 1 x 2 1 Now, y = u v ⇒ dy dx = du dx dv dx 1 Let u = log x cos x ⇒ log u = cos x log log x ⇒ 1 u du dx = cos x × 1 x log x log log x sin Find an equation of the tangent line to the curve (x^2)(e^y)(ye^x)=4 at the point (2,0) asked in CALCULUS by payton Apprentice implicitdifferntiation If y=√ (x^21)log (1/x√ (11/x^2), find dy/dx Sarthaks eConnect Largest Online Education Community
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Find dy/dx y = natural log of x^2 y = ln (x2) y = ln ( x 2) Differentiate both sides of the equation d dx (y) = d dx (ln(x2)) d d x ( y) = d d x ( ln ( x 2)) The derivative of y y with respect to x x is y' y ′ y' y ′ Differentiate the right side of the equation Tap for more steps Differentiate using the chain rule, which states that Share 1 VarunRawat answered this We have , y = log x cos x x 2 1 x 2 1 Let y = u v ⇒ dy dx = du dx dv dx 1 Now , u = log x cos x ⇒ log u = cos xSolution for Find dx y = 4 In x9 log 4x dy (Type an exact answer) dx Q A ferris wheel is 35 meters in diameter and boarded from a platform that is 1 meters above the groun A As per our company guidelines, we are supposed to answer only the first 3 subpartsKindly repost o
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If dy/dx=2y^2 and if y= 1 when x=1, then when x=2 y=? Ex 53, 11 Find 𝑑𝑦/𝑑𝑥 in, 𝑦 = cos–1 ((1− 𝑥^2)/( 1 𝑥2 )) , 0 < x < 1 𝑦 = cos–1 ((1− 𝑥^2)/( 1 𝑥2 )) Putting x = tan θ ySolutionShow Solution It is given that `y=log xsqrt (x^2a^2)` Differentiating equation (1) with respect to x, we get `dy/dx= (1x/sqrt (x^2a^2))/ (xsqrt (x^2a^2))` `dy/dx=1/sqrt (x^2a^2) (2)` `xdy/dx=x/sqrt (x^2a^2) (3)` Again differentiating equation (2) with respect to x, we get
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If y = 2^x, find dy/dx Q If y = 2^x, find dy/dx ANSWER 1) Take Logs of both sides of our equation y = 2^x So we get log (y)=log (2^x) 2) Apply relevant log rule to rhs Log rule log (a^b) = b log (a) nb the dot between b and log (a) represents x / multiply / times ) So we get log (y) = x log (2)
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