State whether the function f has an inverse. Iff 1 exists, find the rule for f-1(x) and show that f(f-(x))=f¯'f(x))=x. f(x)=3x-5 The function inverse.

Q: For the function f(x) = 4x- 3x +2x +6x +2, find f"(x), the third derivative of f, and f''"(x) = %3D

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Q: Write the first and second derivatives of the function f(x) = x3 - 3x2 29x f'(x) f"(x) = Use the…

A: Given function is

Q: Find the first derivative f' and the original function ƒ. f"(x) = x³ - 16x + 4, f'(0) = 3, ƒ(0) = 2…

A: Solve the following

Q: Use the derivative to determine whether the function is strictly monotonic on its entire domain and…

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Q: Find the derivative of the inverse function s(x) if f(x) = -x+ 1 1 r + 1

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Q: Find the first and second derivatives of the function  f(x)  = x4  - 3 x3  +16 x

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Q: Given f(x) = x² + 1, x 2 0, Find the derivative of the inverse at the point (5, 2) (do not find f-1)

A: Let's find.

Q: Find the derivative of f(x) = (2 - 3x) (-5x + 4). O 2 О 22-30х О зох + 22 30x + O 15x + 8 None of…

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Q: find the derivative of f(x) = x2 – 3x + 4, and then 3) evaluate f '(2)

A: Given : f(x) = x² - 3x + 4

Q: x4 -5 7) f(x) = In %3D

A: fx=lnx4-5x first, simplify the function  f(x)=lnx4x-5x f(x)=lnx3-5x now take derivative

Q: Find the derivative of the function. g(x) = 2(3 - 8x) g'(x)=

A:

Q: If f(x) = 3 + x + ex , find ( f-1)' (4)     The derivative of the inverse in 4

A: The given function is,                  f(x) = 3 + x + ex We want to find the value of (f-1)'(4). We…

Q: Find the derivative of f(x) = 33x-1 O 33x-2 In3 O 33x-1 In3 33x In3 32x In3

A: (1). Given: fx=33x-1   As we know that; The Power law; ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: Find the derivative of the function. f(x) 1 = - x6 + (x² + 4)(x² – x – 1) + 10

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Q: Find ƒ‴ (x) , the third derivative of ƒ, and ƒ (4) (x) , the fourth derivative of f, for function.

A: To Determine: The third and fourth derivative of fx=x2x+1

Q: Find the derivative of f(x) = e3 (5x² + x)

A:

Q: Give the derivative formula for the function g(x) 2.1X 2 g '(x)

A: The given function is

Q: Write the first and second derivatives of the function. f(x) = 4.2 In x + 9.3 f'(x) f"(x) %3D

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Q: . Y= In (- (x-2)2

A: To solve the second derivative of the function

Q: Find the derivative of the function. g(x) = (1 + 5x)5(4 + x – x²)7 - g'(x)

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Q: Find the third derivative of the function f(x) = (1) / (2x-1)

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Q: Write the first and second derivatives of the function. f(x) = x3 - 9x2 + 27x f'(x) - 18x + 27 f"(x)…

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Q: Obtain the first and second derivative of the following real-valued functions 1. ƒ : R → R, such…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the derivative of the algebraic function.

A: The given function is fx=x41-2x+1.

Q: Find the derivative of the function. 4 2x - x2 f(x) = %3D x2 - 6 f'(x) =

A: given,        fx=-x2-2x+4x2-6

Q: Use the chain rule to find the derivative of f(x)=3e^−4x^9+3x^3   f'(x)=

A:

Q: Use a computer algebra system to find the derivative of the function.

A: g(x)=x+1x+22x-5

Q: Let f(x) = }x² – x³. Find the value(s) of x if the second derivative f" (x) equals zero.

A: Use the formula, ddx(xn)=nxn-1 to calculate the derivative. Differentiate f(x) with respect to x to…

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. f(x) = 5x2 + 4x + 5 O 5x + 4 O 10x2 + 4x O 10x O 10x + 4

A: Given f(x)= 5x^2+4x+5

Q: Let f(x) = 4 −(1/3)x3 . Determine the derivative (f -1)'(x) of the inverse function to f.

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Q: Find the derivative of the function. g(x) = x" + 4x° – 5x-9 gʻ(x) = D %3D

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Q: Use the Product Rule to find the derivative of the function. g(x) = (x² – 6x + 7)(x³ – 1) g'(x) =

A:

Q: Let f(x) = 4 – x³. Determine the derivative (f-1)'(x) of the inverse function to f.

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Q: Find the derivative of the function by first expanding or simplifying the expression. f(x) = (5x-…

A: Differentiation of the function with respect to x helps to find the derivative of the function.…

Q: Find the derivative of the given function. f(x) = (2 - 5x³)-2 1 f'(x) (2– 5x)-2 5x* 3

A: We have to find derivative

Q: Find the derivative of the given function. f{x) = (9 = 4x³)-2 Let f(x) be expressed as the…

A: our objective is to find the derivative

Q: Find the derivative of the algebraic function. f(x) = (x3 − x)(x2 + 2)(x2 + x − 1)

A: Given information: fx=x3-xx2+2x2+x-1

Q: 1 If f(6) = 3, and f'(6) 2 Let f'(x) be the inverse function of f(x). (f ')'(3) = Write the equation…

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Q: Find the derivative of the function. f(x) = (x² + 8) In(x) f'(x) =

A: In this question we need to find a derivative of the given function

Q: Use the Product Rule to find the derivative of the function.                          g(x) = (2x −…

A: Given:gx=2x-31-5x

Q: Find derivative of q=(X^2-x+1)/x+1

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Q: Find the first and second derivatives of the given function. f(x) = 8x3 – 5x? + 7 f'(x) = f"(x) %3D

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Q: Let f(x)=4-1/3x^3. Determine the derivative (f^-1)'(x) of the inverse function to f.

A: Derivative of inverse function is

Q: Write the first and second derivatives of the function. f(x) = x3 - 6x² + 29x f'(x) f"(x) Use the…

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Q: 1 Find the derivative of each function: b) f(x)=(x'+3x² +7)° 2x+1 b) f(x)=- (x+2x)°

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Q: Find the derivative of the inverse of the given function at the specified point on the graph of the…

A: To sketch the graph of the function f(x) and determine the value of the derivative of inverse of the…

Q: Find the derivative f'(x) for the function f(x) = x² + x – 17. - O A. f'(x) = 2x – 16 В. f («) — 2а…

A: Find the derivative of f(x)

Q: The derivative of f(x) = x³e2x is

A:

Q: Use the derivative to determine whether the function is strictly monotonic on its entire domain and…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.