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

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: 1. If y = x³ + x - 5 then what is the derivative of y with respect to x?

A: Derivative of a function

Q: Solve for the 4th derivative of function K K= x3Cos√x

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Q: 5. Find the derivative of: a. f(x) = cos(e³x-4)

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Q: Find the derivative of the function.

A: We are given with the function g(x) and need to find the derivatives

Q: Find the derivative of the function g(x) = x3/e2x

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Q: What is the derivative of the function f(x) = e-2x?

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Q: 1. Find the derivative of f(x)= x(a+1), given a is a constant.

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Q: Find the derivative of the function g(x)=e^x/3−5x g'(x)=

A: Apply rule of u/v.

Q: Suppose that f'(0) = 2. Find the derivative of the function (e2z – 2x)f(3x) at x = 0.

A: Given that f'(0)=2.Our Aim is to find the derivative of the function (e2x-2x)f(3x)-(i) at x=0.

Q: y = In- e 2x+1

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Q: What is the derivative of y e2x –1

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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 derivative of the function f(x) = ln(e" + 5).

A: We have to find the derivative of the function -          f(x)=ln(ex+5) Here , we will use the…

Q: Find the derivative of the function g(x) et 2 – 2x gʻ(x) =

A: We have to find derivative

Q: 6. Determine the derivative of the function with respect to x. y = x2 – V2x +1

A: Solve the given problem.

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: Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

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Q: Find the derivative of the function.

A: Some important derivative formulas: 1. d(lnx)/dx = 1/x 2. d(√x)/dx = 1/(2√x) 3. d[N/D]/dx = [D*(N)'…

Q: Consider the derivative function h (x) = 5x³ + 3x² – 4x + 4. What is the general antiderivative of…

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

A:

Q: 3 Find the first derivative of f (x) = 3x e

A: Given that : f(x)= x3 / e3x. Find the first derivative of this function. We know that d(xn)/dx =…

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: 9. Find the derivative of y = xe3-x (A)e3-x? (B) 0 (C) e³-x*(1– 2x?) (D)–2xe³-x² (E) e3-x*(1+ 2x²)

A: Given : y = xe3-x2

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

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Q: Find the derivative of the function.

A: To find derivative of the function y=e2xe2x+1. Solution: Quotient rule of differentiation states…

Q: 4) Find the derivative of each function. a. f (x) = In(x² – 4) In e c. f (x) = b. f (x) = x² ln x

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Q: f(x) = e*

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Q: 11 8 Find the derivative of the function: y = 3(x – 4)' x-4

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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 the function. y = 4x e -2x – 4 e x5

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Q: 2. Find the derivative of (a) f(x) = x* + 4x 2 + 4e" (b) f(x) = 2 tan (x) – 6"

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

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

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Q: Find the derivative of the function. f(x)=4tan-1(e9x)

A: Consider the given equation

Q: Find the derivative of f(x)=

A: We use the quotient rule of logarithm to simplify the expression

Q: Find the derivative of the function. 2 1 3 h(x) x3 h'(x) =

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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: Find the derivative of the function. h(x) = ln(2x2 + 1)

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Q: 2. Find the derivative of (a) f(x) = x* + 3x 2+ 4e" 4 (b) f(x) = 2 tan(x)- 2"

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the derivative of the function g(x) et 2 + 3x g'(x) =

A: Given: gx=ex2+3x

Q: Find the anti-derivative of g'(x)= log1/2(X)

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Q: Find the derivative with respect to x of h(x) = e2x²+6 In(x).

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Q: 10. Find the derivative of y with respect to x. y=(x^(6)lnx)^(4)

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Q: Find the derivative of the function. f(x) = e-4x

A: The given function is:fx=e-4x

Q: Determine the value of the derivative function for Ax) = (x + x)(x- 2) at x = 2. %3D A 6 в О с 5 D1

A: