Find the derivative, dy/dx: y = log3 (2x +1) Oy =- (2z+1)3 In 3 Oy = (2r+1) In 3- Oy= log, e (2z+1)3 loga e Oy 2+1

Q: t du/dt = u - u2 ln(t)

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Q: du/dt = (1/ln(t+u))  -1

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Q: Consider f (x, y) = log(r² + y²) f.(x, y) = %3D and fy(1,0) = %3D

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Q: Q1/ Find dy/dx for the followings functions: 3 x(x+1)(x-2) 1) y = use logarithmic differentiation…

A: From the given problem:   y=xx+1x-2x2+12x+33   Now we can simply write as:   y=xx+1x-2x2+12x+313…

Q: If x = tan - log y a d'y dy Show that (1+x²)- +(2x- a)-0 dx dx?

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Q: Find the derivative of f(x) = e* (3x' - 4) %3D

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Q: Find the derivative of f(x) = log, (x° + x – 1). %3D 2 + x - 1 f (2) = %3D (3z* + 1) (In 2) (3z +1)…

A: Given:     fx=log2x3+x-1

Q: dr 1- y = Inlog 2- y = (cos x)*Snx 3- у e (sinx

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Q: Find for y = (x? + 5)°(1 – x*)* using logarithmic differentiation. dx

A: To find dy/dx using logarithmic differentiation

Q: Find dy/dx by implicit differentiation   √(x + y) =  1 + x2y 2

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Q: xy + e^y = ln(x + y) defines y as a function of x implicitly for the most part. Express dy/dx in…

A: Given an equation, Where y is a function of x.

Q: Use logarithmic differentiation to find dy/dx. y = x6/x, x>0 dy dx - (x²-6) (lnx + x = 6) X

A: Given function

Q: Show that the derivative of ! log (9-1)(g-1)u²+2u–1 u e [0, 1], q 2 3 > 0 for u > 1+(q-1)(2–u)u

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Q: F(x) = "(5t - 1) dt %3D

A: We need to find the first derivative of F(x)=∫x2x(5t-1)dt. By Leibniz's integral rule,…

Q: Explain why the derivative of y = logakx, k > 0, is dy/dx = 1/xIna for any constant k. (the a is the…

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Q: Use logarithmic differentiation to find dy dx y = (x + 1)(x-6) (x - 1)(x+6) dx X>6

A: By using logarithmic differentiation to find dydx.y=x+1x-6x-1x+6, x>6