Find the inverse function of the f(x) = 5x + 10. O a. f'(x) = 1/10(x) + 2 O b.f'(x) = 1/10(x) - 2 O c.f'(x) = 1/5(x) – 2 O d. f'(x) = 1/5(x) + 2

Q: Find the first derivative of g(x) = - 5 In(x)cos(r"). g'(x) =

A:

Q: find the n-th derivative of f(x). f(x)=e^-2x

A: Given function is fx=e-2x. Chain rule of differentiation states that: ddxfgx=f'gxg'x Now, we find…

Q: Find the derivative of the function.

A:

Q: Find the derivative of the function. f(x) = ln(5+e^x/5-e^x)

A: Use derivative formula :- f(x) = lnx then derivative f'(x) =1/x

Q: Find the derivative of the function. 2 a) f(x) = x² ln(x) b) g(x) = 2" + log, (x + 5) +ez c) y =…

A: We have to find the derivative.

Q: Find the derivative of the composite natural exponential functions 1. f(x) = In( 2. g(x) = In(v³ +1)…

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Q: Find the derivative of the function.

A: We know that, logbx=y if and only if, x=by. Also, logbxn=nlogx

Q: Find the first derivative of y with respect to x for the following :functions b- y = In( 3x .e-*)

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Q: Find the derivative of the function h(x) = log5 (x/x − 1)

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Q: The derivative of y= xh* is O 1) (In x)(xh*-) O 2) 2 an x)(xh*) O 3) (In x)* O 4) xhx

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Q: Find Find the second derivative of the given function. y = In(x² – 1)

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Q: Find the first derivative of the function g(x) = V5 +x +4cos (2x).

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: Find the derivative of f(x)=x^2 e^2.5x

A: Given problem:- Find the derivative of f(x)=x2 e2.5x

Q: Find the derivative of the function

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Q: b) Find the derivative function of f(x) = √5x - 1 using first principles.

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Q: 26 Find the 155th derivative of (1 + x°)" at x = 0.

A: see 2nd step.

Q: compute a formula for the nth derivative of f(x)=e2x

A: We have givenWe have to find a formula for nth derivative of f(x)

Q: 1. Find the derivative of the function f (x) = e2x + 5* + x3

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Q: Find the derivative of the function y = In(8 – e-a f'(x) =

A: We have to find derivative

Q: Find the derivative of the function. (x) = In(4 – x®) r"(x) =

A: We have to find

Q: Find the second derivative of the function. f(x) = (3 + 2x)e−3x

A: Given:The given function is f(x)=(3+2x)e-3xTo find:The second derivative of function f(x)

Q: Find the derivative of the function f(x) = log23√(2x + 1)

A: To find derivative of fx=log22x+13

Q: h(x) = e(-1/2)x

A:

Q: Determine the 3rd derivative of the function y=x3/x+2 at x=−1.

A:

Q: Find the derivative of f(x)=(x+4)e^(5x)

A: We have to find the derivative of f(x) ,where f(x) is given by

Q: Find the second derivative of the function.

A: Given the function: g(x)=x + ex  ln(x) We have to find the second derivative of the function. Let's…

Q: f. y=In(x8+1)

A: We will solve the problem

Q: find the first derivative of   F(x) = e(x+5)

A: Given,

Q: Find the second derivative of the function. g(x) = 9/x + e6× In(x) g"(x) = %3D

A:

Q: Find the derivative of the function. y= log , (3x2 - 2x) 5/2 O A. In 9(3x- 1) (3x2 - 2х) OB. 10(3x –…

A: We need to apply 1.chain rule 2.differentiation of logarithmic   we get option c as correct answer

Q: 3 Find the derivative of the inverse of f(x) = x +1 using the formula dy %3D 1 off "(x)= g'(x)= dx…

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Q: Find the derivative of the composite natural exponential functions 1. f(x) = In x² x-2 2. g(x) =…

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Q: ) .3 Find the derivative of h(x) = cos (2x – 5 %3D

A: Given,            hx=cos42x3-5To find : The derivative of the given function.

Q: F(x)=In(52x+n • (x+2) ) %3D

A: Find the derivative of the function

Q: Find the derivative of the function. f(x) = ln(x − 1)

A:

Q: Find the derivative of the function. f(x) = e In( Vx + 8 f'(x) =

A: Given, f(x) = ex ln(x+8) We have the formulas d(ex)/dx = ex                       ...........(1)…

Q: find the second derivative of y = x In x A 1/x в) 1/2х D) 2x

A:

Q: Find the derivative of f(x)=(x−2)e^(−3x).

A: The first derivative of the function f(x) = (x−2)e−3x is calculated as follows.

Q: Find the derivative of f (a) = e" (x² + 2).

A:

Q: Find the derivative of y= (x³-1) /(x-1). O a. 2x -1 O b. 2x -3 O c. 2x + 3 O d. 2x + 1

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Q: What is the first derivative with respect to x of the function g(x) = 3/9x O 1/2 9.

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Q: Find the derivative of the function. f(x) = ln x/(x2 + 1)

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Q: 1 Find the derivative of the function : ƒ(x ) = V |2x + 3

A: The given function is: f(x)=12x+3 Let, u=2x+3. So, f(u)=1u=u-12 and u=2x+3

Q: Find the first derivative of g(x) if g(x) = e²* In(2x) %3D

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Q: find the derivative of f(x)=(x^4+3x^2+8)cos

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Q: 11.Find the derivative of the functions: a) f(x) = In(9x²2 – 3x) b) g(x) = In(ln x)

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Q: 8 Find the derivative of f( x ) = x° log, (x + 3). f'(x) : = (x).f

A:

Q: 1. Find by implicit differentiation for xe = 2xy + y³.

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Q: Find the derivative of the function f(x) below. f(x)=ln(5−e^(−4x)) f′(x)=

A: Explanation: Given that, f(x)=ln(5-e-4x) Differentiate both sides with respect to x.…

Q: What is the derivative of the function h(x) = ((4x^2-4)/(cos(x)))^8

A: We have to find the derivative of ((4x^2-4)/(cos(x)))^8 = 4^8(x^2-1) sec^8(x)= 65536(x^2-1)sec^8(x)