EXERCISE 3. Derive a formula for the nth derivative of f(x)

Q: 1: Using the definition, calculate the derivative of the following function. S(x)=4-x²

A: Topic:- derivatives

Q: -What is the derivative of (x + 1)2 ? a) x? + 2 b) x c) x d) 2x+2

A: We will use chain rule of derivative

Q: f (x) e1/x x2

A: Given function is fx=e1xx2

Q: 3. Find the derivative of g(r) = Do Not Simplify. +1

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Q: 3. Find the first and second derivatives of the function f (x) = e¬²

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Q: 3 Find the derivative of f(x) = x°e*.

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Q: 2 a) For the function f(x) = X-3 , find f'(1) by using the definition of derivative.

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Q: 9. [Essay] Find the derivative of y = 3x + 1). За* (x? — Зх + 1). Зах

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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: following

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Q: -3x Suppose . What is the correct result of the derivative of h with respect to x?

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Q: 2 Using the definition of derivative, prove the following: (a) f'(x) = x if f(x) = x %3D

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Q: (14 Find the derivative of the function 7 (^ Y = x²+3 15 x²-3

A: Find the derivative of the function  y= [(x2+3)/(x2-3)]5

Q: x+D メD

A: To Determine: we have a function then find the derivative Given: we have a function Z(x)=Hxx-D2+x2…

Q: 1. Find the derivative of each function. i] f(x) = e*=*

A: Here f(x)=ex2-πxddxf(x)=ddxex2-πx=ex2-πx ddxx2-πx=ex2-πx 2x-πHence, ddxex2-πx=ex2-πx 2x-π

Q: Calculate the implicit second derivative of b(z)=(x-5)^2 find the value of b''(-1

A: find the second derivative of the given function

Q: g +2 Find the derivative of h(x) = ln

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Q: Find the derivative of the algebraic function.

A: Given: f(x)=4-3x-x2x2-1

Q: a) Find the derivative of g(x) = 3tanx – 4cotx. %3D b) What is the value of g 3.

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

A: We have to find

Q: Q2/ Find the derivative of the function f(x) = V3x +1 by definition %3D

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Q: 9) Find the derivative of each function a)f(x) = x'e* %3D

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

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Q: Vhat is the second derivative of f(x) = x'e? II

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Q: Determine the first derivative of the ff. function x? + 1) y = V1 + In x

A: y=x2+11+lnx

Q: calculate the derivative. g(x) = e2

A: We know that the derivative of a constant is zero. This result is used to prove the given statement.

Q: Find the derivative of f(x) = e2" (3a? - x)

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Q: 4) Find the third derivative of g(x) = e*.

A: We will solve the problem

Q: (A) Find derivative of y = In V4+ a2

A: Given that a function y (x) and we find derivative of this. We know that : d(lnx)/dx = 1/x . Here i…

Q: Find the derivative of the function. u(x) = (x² + 1)3³ ? - 1

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Q: Using the definition of derivative, find the derivative of the following functions: (a) y = xvx² -2…

A: (1) Y = X*(X2-2)0.5       dY/dX = (X2-2)0.5  + (1/2) *(1/(X2-2)0.5) *…

Q: A. Find the derivative of the given function at a given number 1. y =3x -2 at f(1)

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Q: Find the second derivative of the following function: f(x) = esin1, %3D

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Q: Find the derivative of h(x) = e$ec(x-n)

A: dexdx=ex dsec(x)dx= sec(x) tan(x) d(xn)dx=n.xn-1

Q: Find the derivative of the function. f(x) : et? + 9

A: This question is about finding derivative of function.

Q: Solve for the derivative of the given functions using the Chain Rule formula. Let f(x) = √(x2 + 3x +…

A: (a) fx=x2+3x+1 Inner function : u=x2+3x+1. Outer function : y=u.

Q: 5. a) Find the first order derivative of the following function. y x° In x

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: Obtain the derivative of the function f(2)% 3 -3a° – a* + 4x. Enter your answer as a function of a :

A: Given that f(x) = -3x2 - x4 + 4x  Find derivative of this function f(x). We know that derivative of…

Q: Find the derivative of the function. h(x) = log,(x² + x) h'(x) %3D

A: Given query is to find the derivative of the expression.

Q: 1 :) 100 is equal to The derivative of the function esin x

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Q: 4. Find the second derivative of the function. Simplify if possible. f (1) = 2+5

A: topic - derivative

Q: Find the derivative of ?, implicitly of  BY SHOWING ALL STEPS When N=11 and M=3

A: Given that lnMxy-tanNx+My=e-M-MyN And N=11 and M=3

Q: Calculate the derivative. g(x) = e2

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Q: 8. Find f '(2) if f(x) = [g(x)]*, and g(x) = x + 2

A: g(x) = x+2  f(x) = [g(x)]4  f(x) = (x+2)4

Q: 4. The derivative of the function f(x) = r +3) is

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Q: 2. Using the definition of derivative, prove the following: 1 (a) f'(x) =E if f(x) = V

A: The given function is  f(x) = x1/3 To find f'(x)

Q: A1) Using the definition of derivative, find the de

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Q: 2. f(x) = 2x – 5x%

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Q: 2. Consider the function f(x) = e¯*. -2x (a) Show that the derivative is f'(x) = %3D

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