Let f (x) = x e>x. Find a formula for the nth derivative of f, where n is any positive integer. Use x and n in your answer if needed. f(n)(x) = (n-1) ex + 5"xex n·5

Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

A: Find your answer below

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: Q1:- Find the first order derivative of each of the following functions: e) y = 1 + x'nx

A: Given that y = 1 + xlnx . We find its first derivative. We know that d(xn )  /dx = nxn-1  Here i…

Q: Find the derivative of the function F(s) = In(9 ln(8s)). F'(s)

A:

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

A:

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

A:

Q: If f(x)=In(x-1), find the formula for f^((n))(x), the nth derivative of function f(x) f(x) = ln (x –…

A:

Q: - 3x Find the derivative of y with respect to x if y = e

A:

Q: 1. Find the derivative of the following function: f(x) : (x² sin- if x ± 0 if x = 0

A:

Q: Find the derivative with respect to x if f(x) = e -14x The derivative with respect to x if f(x) =…

A:

Q: Find the derivative of the function. g(x) = e¯x + 3e2x – 1e-x + 17

A: Use the property for the exponents to simplify the function g(x).

Q: Find an expression for the derivative of h(x)=ln(f(x)). answer in terms of f and f'.

A: The given function is  h(x) = ln(f(x))

Q: - 17x Find the derivative of y with respect to x if y = e 口

A:

Q: Givenf (x) = ln x, what is the derivative function f' (x), and what is its domain? f' (æ) = e², for…

A:

Q: Find the derivative of the functions below: In(x) (a) g(x) = log,(x) g'(x) = (b). y- in(6x®)

A:

Q: Find the derivative of y with respect to the independent variable. x8)n 5) y =log 5 x-8

A: using the fact of logarithmic  logax=lnxln(a) find the derivative

Q: e3x-e-3x Y = e 3x+e-3x 4. t2 y= 72-1 5. X = t-1

A:

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: The derivative of the function 3+ln x is: y = cos(In x)

A: y=3+ln(x)cos(ln(x)Differentiate w.r.t.xApply the Quotient Rule:  fg'=f…

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). h(x)=…

A:

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

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: Let f (x) = e10x. %3D Find a formula for the n-th derivative of f, for n 2 1.

A:

Q: Find the derivative of the function.s(x) = e3x − 1/x3 − 1

A: The given function is

Q: Find the derivative: h(x)= 3 tan*(e²*)

A: Question based on derivatives application.

Q: Find the derivative of the function. y = e In(7x)

A:

Q: In the given question , use the alternative form of the derivative to find the derivative at x = c,…

A: g(x) = x2- x, c = 1

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

A:

Q: Let f be the function defined for x > 0, with f (e) = 2 and f', the first derivative of f , given by…

A: Given, f be a function defined for x>0 and the derivative of f is f'x=x2lnx Point e, 2

Q: Find the derivative of f(x) = In (x* V8 – 6x), using the properties of the logarithm. Provide your…

A: I have stated the used formulas in the solution

Q: Find the derivative with respect to x if f(x) = e 2x %3D The derivative with respect to x if f(x) =…

A:

Q: Find the derivative of the function. g(x) = 500(5 – e-0.1x)

A: Given,           g(x)=5005-e-0.1x

Q: h(x) = (cos x)(4x²– 3)

A: Explanation of the answer is as follows

Q: Find the derivative of the function y, below. y = 6x(ln a + In 5) – 8x + e ||

A: Given that y=6x(lnx+ln5)-8x+e To find the derivative of y

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

A:

Q: Find the derivative of the following function, 1 f(x) = e* + In(x). x² -

A:

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

A: fx=e2x3

Q: Which of the following is the derivative of the function f (x) = 5x · e*? Of (x) = 5e* Of'(x) = 5e*…

A:

Q: Find the second-order derivative of the following function: f(x) = log2 cos x + ln π

A: We have to solve

Q: Solve for the derivative of the given functions using the Chain Rule formula. Suppose f(x) =…

A: Given, f(x)=sin(2x)+17

Q: Find the derivative of the function. f(x) = 2 tan (e11x) f'(x)=D

A: We have to use Chain rule of differentiation.

Q: Find the derivative of the following function 1. f(x) = 5x' - 32x + e?

A:

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

A: Consider the given equation

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

A:

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

A: Given : x2+3xy+y2 = 4

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

A: The given function is:fx=e-4x

Q: Find the derivatives of following functions e2x f(x) 1- ex

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…