Differentiate the function. y = (In(1 + ex))8 y' =

Q: Find the derivative of y = 6e x – cosx.

A: Given function, y=6ex-cosx Used formulas, ddxcfx=cddxfx  c=constantddxex=exddxcosx=-sinx

Q: Find the derivative of function.

A: Find the derivative of function. y=(ln|x+1|)4

Q: Find the 4th-order derivative of the function y=xsinhx.

A:

Q: Find the derivatives of the functions in Exercis y = xe-x + ex3

A: y=xe-x+ex3

Q: Find the 3rd derivative of the function y=xsinx

A:

Q: Find the derivative of the function. y = esin(5x) + sin(e5x) y' =

A: The solution are next step

Q: find the derivative of y with respect to xas appropriate.11. y = ln 3x + x              12. y = 1/ln…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Find the first derivative for y = 5 cos x

A: Given,          y=5cosx

Q: In y=e³ sinx

A:

Q: Find the derivative of the functions. y=cosh^-1 (3x)

A: We have to find derivative of the function: y=cosh-13x Rewriting the function, y=cosh-13xcosh y=3x…

Q: Find the derivative of 3 In xy + sin y = x².

A:

Q: 5 Calculate the second and the third derivative of y = 6x – y": y"

A:

Q: Find the derivative of the function. y = 2 cos5 x

A: Given, y = 2 cos5 x To evaluate, dydx

Q: Calculate the derivative of the function y=1+cosxsinx.

A: Given: y=1+cosxsinx we know that for finding derivative of given function we need to use product…

Q: 8. Find the derivative of the function. y= In(1+x)

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Q: Calculate the 4th derivative of the function y=x2/x−1 at x=2.

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Q: Find the derivative of the function. y = sin-(2x + 1) y' = %3D

A: We need to evaluate the derivative of the following function y = sin-12x+1 Formula Used : ddxsin-1x…

Q: Calculate the second derivative y : Vx - /y = 1

A:

Q: Find the derivative of the function

A: Given:y=arctanx+x1+x2Differentiate formula:ddxarc tanx=11+x2ddxuv=vdudx-udvdxv2

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 derivative of the function.

A: Consider the given function as y=xtan-12x-14ln1+4x2

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

A:

Q: Find the derivative of the function y = x² cosh²3x

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Q: Find the derivative of the function. y = In(x?)

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Q: Find the derivative of the function.

A: The given function is y=x2-sin2x4

Q: find the first order derivative of the function

A: We have to solve

Q: Find the derivative of the function. y = In(Icsc(7x)|) y'(x) =

A:

Q: Find the nth order derivative of the square root y=√x.

A: Let's first calculate the nth order derivative of the power function y=xm where m is a real number.

Q: Find the derivative of the function.

A:

Q: Find the derivative of y: 1- y = (cos 0)V2 Cos O 2- y = 7sec ln 7 3- y = 2sin 3t

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Q: Find the derivative of the function y = 2x − cosh √x

A: The given function is y=2x-cosh x. Obtain the derivative of y=2x-cosh x as follows.

Q: 7. Find the nth derivative of y = 1//x.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 6. y = vx sin-'(x)

A: we havey=x sin-1(x)

Q: Find y" by implicit differentiation. 5 + y = 6 5x

A: Please refer to the image below

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

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Q: Find y" by implicit differentiation. 3x + y =5 3r y

A:

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

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Q: Find the derivative of the function. y = sin2(x2 + 2) y' = %3D

A:

Q: 1) Find the 3rd derivative of y = sin(x) %3D

A: To find the 3rd derivative of y=sinxx. Solution: For finding third derivative, we need to find first…

Q: Find the derivative of the function. y = etan(8) y' =

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Q: 7) y=cos/2x+1

A:

Q: Find the first derivative of y = cos*x- sin*x.

A:

Q: 3. Find the derivative of: y = csch¬(In (sech(sec()))).

A: Note:Two questions submitted simultaneously, kindly upload question 2 separately.

Q: Find the derivative of the function. 9 y =- Vx + 1

A:

Q: Find the 3rd derivative of the function y=exx.

A: Differentiating with respect to x, we get Again differentiating with respect to x, we get

Q: Find the nth order derivative of the cube root y=3√x.

A: We first find the first three derivatives using the power rule

Q: 2) Find the first derivative of y = sec1(2e3*)

A: To find the first derivative of the given function.

Q: Find the 1st derivative of the function: y = 4(Vx + 1)5

A: Given that: y=4(x+1)5

Q: calculate the derivative y = (sinh−1(x2))3

A: Given The chain rule of derivative is given by: The derivative of the inverse hyperbolic function…