Suppose f-1 is the inverse function of a differentiable function f, and given that G(x) = 1/f-1. If f(3) = 2 and f'(3) = 1/9, find G'(2).

Q: Find the derivative of function f given by S(1) = =! X-1 3 x+3'

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Q: 4) f(x) e**+6x

A: If F(x) = f(g(x)) , then F'(x)= f'(g(x)).g'(x). dexdx=ex dxndx=n.xn-1. Quotient Rule of…

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: If f(1) = 3, f'(1) = 4, g(2) = 2, and g'(2) = 8, find F'(1). F'(1) = ... NOTE: This problem is a bit…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Consider y = f(x)=√1+2x, x 2-1/2. Without finding x = f(y) explicitly, find the derivative of the…

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Q: Find the derivative of the function. 2 a) f(x) = x² ln(x) b) g(x) = 2" + log, (x + 5) +ez c) y =…

A: We have to find the derivative.

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

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

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Q: If f(x) = (x® – x4)%, then the 31st derivative of f(x) is 0. True O False

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Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: Given that the function f(x) = | x - 1|

Q: need fast

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Q: Suppose that the differentiable function y = ƒ(x) has an inverse and that the graph of ƒ passes…

A: Given,

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: For what values of x is the derivative of the function Vx2+ Vx equal to 1?

A: Given,           The derivative of x23+x3 equal to 1.

Q: Find the derivative of the function

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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 y = In(8 – e-a f'(x) =

A: We have to find derivative

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

A: We have to find

Q: Let y = f(x) = x² +1, evaluate the derivative of the inverse function x = f-l(y) at y = 2.

A: Given a function, y=f(x)=x2+1 To find the derivative of the inverse function of f(x).

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: Compute the derivative of the given function. f(x)=−4x^π+4.1x^1.3+π^1.3

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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 derivative of the inverse of f(x)= x° +1 using the formula dy 1 off "(x)= g'(x) =- f'(g(x))…

A: Topic:- application of derivatives

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

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Q: Suppose that a function f(x) has derivative f' (x) = g(x)+ h(x) for some functions g(x) and h(x).…

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Q: Find the derivative of function defined as follows. h(x) = (x2 - 1)3

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Q: Suppose f(-3) = 3, f'(-3) = 5, = -8, and %3D g(-3) = 1, gʻ (-3) = H(x) = f(x)e®(x). Find the…

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Q: if f(x) = x²√√In x² P x A. f'(x) = . find the derivative of this function f'(x) 1-In x² x²√√In x²…

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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 the given function F(x)=  x+1/x-1

A: The given function

Q: 3 Find the derivative of the inverse of f(x) = x +1 using the formula dy %3D 1 off "(x)= g'(x)= dx…

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Q: f(x) = e*

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

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Q: Find the derivative of the function. 4 f(x) x In(x) f'(x) %D

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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: f(x)=ln[x^2÷(x+1)^3

A: Formula:

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

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

A: Consider the given equation

Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=4f(0)=4 and…

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Q: Find the derivative of the function g(x)=e^x/2−4x g'(x)=

A: Here we need to apply chain rule of differentiation. We have Derivative of e^x is e^x.

Q: Find the derivative of the function g(x)=e^x/2+5x g'(x)=

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Q: 8 Find the derivative of f( x ) = x° log, (x + 3). f'(x) : = (x).f

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Q: x +2 f(x)= x - 3

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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 inverse function for y=x⋅3x provided x>0.

A: