The derivative of the function f(x) = 5+ ln r is: 1 a. f'(x) = 2.x/5+ In x b. f'(x) = 2/5+ In x In x 2x/5 + In x c. f"(x) = a

Q: What is the first derivative of s(x)=(7x)3x at x=4?

A: To evaluate s'(4)

Q: In y = 22 cosh1 2x

A:

Q: calculate the derivative with respect to x. ln(x2 + y2) = x + 4

A: Given function lnx2+y2=x+4 Differentiate the above function w.r.t 'x' ddxlnx2+y2=ddxx+4…

Q: 3.

A: Indefinite Integration

Q: Find  dy dx by implicit differentiation. tan−1(4x2y) = x + 5xy2

A: tan−1(4x2y) = x + 5xy2 We differentiate both sides with respect to x using the product rule and…

Q: Compute the derivative of f(x) = 7 ln (x + 10) + In (x³ ): Answer: f'(x) =

A: Given function is  f(x)= 7ln(x+10) + ln(x3), we have to find the derivative of f(x) with respect to…

Q: ) y = In³ )) (tanh²(scc '(x²)

A:

Q: Find the derivative: y = x [ln(x) - 1] O ln(x) - 1 о O x ln(x) O In(x) O 1 + In(x)

A: Given y=x[lnx-1]To find dydx:

Q: Compute the high-accuracy central difference approximation for the first derivative of y = cos x at…

A: There are three types of approximations to the derivative of a function f(x) at a point a. They are…

Q: Compute the derivative of the function y=x2/ln x at x=e.

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Q: Find the derivative: y = 6 In x 6 ln x-1 x7 1-6 ln x 12 1+6 ln x x12 4 O 1-6 ln x x7 O

A:

Q: 2.Find the derivative of y = In cosh x. %3D

A: Using chain rule of differentiation.

Q: Find the derivative of y with respect to θ, y=6θ(sin(ln(6θ))+cos(ln(6θ))).

A: To find derivative of y.

Q: Find one anti derivative of (x+1)^2 and then find  integral(x+1)^2 dx.

A:

Q: Determine the first derivative of the ff. function y = Vxe2* cos x

A: Derivative of a function gives the tangent of the curve at a given point. Derivatives are used to…

Q: find the first and second derivatives of f(x) = ln (x+1)

A: f'(x)=1x+1 and  f''(x)=-1(x+1)2

Q: find the derivative for  h(x) = 3e ^ -x * ln(2x+1)

A: Using product rule of derivative In order to solve the given problem.

Q: Find the second derivative of g(x) = sinh(x) cosh(x)

A:

Q: Find the derivative of z=(ln5)e^x dz/dx=

A:

Q: Find the derivative of n^(ln⁡(cosu)). Where n=822

A: Given information : nlncosu Here, n=822. we have to find the derivative of given function.

Q: What is the derivative of: y ln x − x ln y = 1

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the indic ed derivative. dz x2 for z = x2 dx 1 - x - 2x2 dz dx

A: Formulas:

Q: Find the instantaneous rate of change of g(x) = In(x + 3) at x =

A:

Q: a the derivative of h(x) = ln + 2 x5 et |

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Q: Find the derivative of f(x) = –4 ln (5 cos (-4x))

A:

Q: find the derivative of y with respect to x. y= ln3x

A: We can solve the given problem using chain rule derivative.

Q: what is the derivative of f(x)=ln(tanhx)

A:

Q: Apply central divided difference approximation (CDD) to find the first 5 derivative of F(x) = e0.8x…

A: To find the first five derivatives of fx=e0.8x when x=24 using central divided difference…

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = 1/ln 3x

A: Given:

Q: Use forward-difference formula to evaluate the first derivative of y = cos(x) at x = using a value…

A: Given we have given the function y=cos(x) we have to find the first derivative of y = cos(x) at x =…

Q: derivative of a Y with respect to x Y= ln (15x)+3x dy/dx=

A: Use formula of derivative to solve

Q: Find the derivative of the function g(x) = ln ex/(1 + ex)

A:

Q: Determine the first derivative of the ff. function a. y = 400(2)*+3 sin 3x b. y = Vxe2x cosx…

A: Given1) y=400(2)x+3sin3x2) y=xe2xcosx3)y=1+ln(3x2)1+ln(4x)We need to find the first derivative of…

Q: Find the 2nd derivative of the given function fCt) = t² Int

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Q: Compute the derivative ln(ex+1) / 2x+1

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Q: Find the derivative of the function f(x) = (3+arctanx)^(ln(x^2 +1))

A: Apply exponent rule:

Q: 4x dx

A:

Q: What is the first derivative of g(x) = ln #*+1? x2

A: Derivative of ln(x):       ddx(ln(x))=1x Division rule of derivative:-…

Q: 1 erivative of x²+2

A:

Q: Find the derivative of the function. 5/1 x+1 In 22 + arctan x %3D X -1· dy dx

A:

Q: is the derivative of In

A:

Q: Calculate the derivative of the function y=log2 x ln (2x) at x=1.

A:

Q: Compute the derivative of the given function. f (x) = 2 ln x – vT

A: Given fx=2lnx-x To find the derivative:

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (ln x)

A:

Q: 1. Find the derivative of g(x): Int dt 1+t Cos

A: This will solve by Leibnitz theorem

Q: Find the derivative of the function. 8 f(x) =x" log 6x .7 ,7 O A. X +8x log ,x .7 O B. In 6 + 8x log…

A: According to product rule of differentiation ddxuv=vddxu+uddxv and according to power rule of…

Q: Find the first derivative of h(x) if h(x) = cos (x – 2x) -

A: h(x) = cos2(x3-2x)

Q: Show that the derivative of f(x) =xln(x)−x is ln(x). Use this to compute∫ln(x)dx.

A: Sum/difference rule of differentiation,

Q: Find the derivative of y with respect to x. Y=(x^2 ln x)^4

A:

Q: Find the derivative of s(*) - L Int dt 1+t

A: