Find the derivative of the composite natural exponential functions 1. f(x) = In( 2. g(x) = In(v³ +1) 3. h(x) = In(x² + 2x – 5)

Q: 1) Find the derivative of the given function with respects to e 3tan ở In 3 y

A: Given

Q: 3. Use logarithmic differentiation to find the derivative of y with respect to the given independent…

A: we have to find the derivative of y by using logarithm.

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. f(x) = ln(5+e^x/5-e^x)

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

Q: 1. Find the derivative of each of the following functions using chain rule: y=3x* (x* -2) a)

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Q: Find the first derivative of y = e3x. 3e3x

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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 first derivative of each function. a) f(x)=ln (e^x+e^-x)

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: The derivative of the function f(x) =x ln x is: a. f'(x) = In x +1 b. f'(x) = ln x +. c. f"(x)= In x…

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Q: II. Determine the derivative of the ff. logarithmic functions 7. y = 12x² log 8x 8. y = In 25x %3D…

A: Solution is below

Q: (A) Find an equation of the tangent line to the graph of f(x)=(4x+1)sin(πx) at the point whose…

A:

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 first derivative of the following functions with respect to x y = In(ln(In x))

A: To find first derivative of the given function.

Q: Find the derivative of the function. 1 + e5x e 5x 3x e

A:

Q: 5. Use the chain rule to find the derivatives of (a) y = log; V4 + 1 (b) y = (x – e-")²

A:

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

A:

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

A: We have to find derivative

Q: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

A:

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: 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: The derivative of In x is and the derivative of a constant C is, sO X dx = In |x| +C for x> 0.

A: Given x>0, The differentation of natural log x is 1/x  And differentation of constant are zero.

Q: Let h be a function that has second derivative (x+ 1) (x – 2) (x + 4)e5 h"(x) Is x=2 the…

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

A:

Q: 2 Compute the derivative f'(x) of the logistic sigmoi 1 f (x) : 1+ exp(-x)

A: We have to find

Q: 1. Find the anti-derivative of the following. e" (x + 1) dx x2

A: From the given information. Anti-derivative has to be calculated to the following expression.

Q: Find the derivative of the function f (x) = /e* – In(x) 12 – 1/x) O (ex12 – 1) O (e2 – 1/x) e? -x)

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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*

A:

Q: 3. Find the second derivative of f (x) = e²/*° and fully simplify your answer.

A: fx=e2x3

Q: 2. Given f(x) = x³ – 2x² + x + 2, find x e (-1, 3) such that f'(x) = 5. 3. Compute the derivative of…

A: Since you have posted multiple questions, as per our guidelines we are allowed to answer the first…

Q: Find the slope of the tangent line to the exponential function at the point (0, 1). y 2 1 (0, 1) -2…

A:

Q: Q3: find the derivative of In(x4+3x-1) a) f(x) = %3D x²+1 b) f(x) = 4x³ . log(x² + 2x) %3D c) f(x) =…

A: Use product rule of differentiation.

Q: Find the derivative of y. x2 =log6 x+1 O A) Sx+1 x2 O B) ) In 6 x2 2x+1 1 Sx+1 In 6 x2 D) None of…

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

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

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Q: 2. Determine the 8th derivative of y with respect to x of the function 1 f(x) = 1+x2 and find the…

A: Taylor series

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

A:

Q: Find the derivative of the given function e5x (2x+1)5 b. f(x) = In Vx²+1 f(x) = (x In x – x)

A: Given that: b. f(x)=lne5x(2x+1)5x2+1c. f(x)=(xlnx-x)

Q: Find the first derivative of the following implicit function: X² + 3xy + y² = 4

A: Given : x2+3xy+y2=4 Lets take first derivative  Take derivative with respect to x. apply the power…

Q: nd the derivative of the function  h(x)=ln(4x^2+3)

A:

Q: 24. Find the first order derivative with respect to x of the function u = log(x+ x .

A: The solution for the above question is as shown below.

Q: Find the first derivative of the following implicit function. x² + 3xy + y² = 4

A: Given : x2+3xy+y2 = 4

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

A:

Q: Find the derivative of the exponential function f ( x ) = 5x 2 e 7x

A: Given function: f(x)=5 x2 e7x     Calculate the derivative of f(x): f(x)=5 x2 e7x   Take the…

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

A: The given function is:fx=e-4x

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: 1- Find the first derivative of y with respect to x for the following functions: In5 7x y = log5 . a…

A: