Find the inverse of the function f(x) = 1+ (1/x), x 0. Then check that f-(f(x)) = f(f-'(x)) = x and that df-1 1 d.x f(x) f'(x)'

Q: f(x) = acos(b\x) x2 COS

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Q: Find the derivative of f(x) = COS 4 log3 (x²) os(5x)

A: Explanation of the answer is as follows

Q: Find the first and second derivatives of the function. f(x) = In(x + 4) f'(x) = f"(x) I3D

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Q: Find the derivative of f(x) = (3x – 2x?)’using the chain rule %3D

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Q: Solve for the derivative of x² – y² = 9 using implicit differentiation %3D

A: Given :                x2 - y2 = 9To find :                 y'

Q: Compute the derivative f'(x) for f(x) = log(x*) sin(x³).

A: Topic - derivative

Q: find derivative of g(x)=integration3x2x (u2-1)/(u2+1) du

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Q: 3x-4 1. y = Arctan

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Q: 1 Use the power rule to find the derivative of f(x) = Vx 15 f'(x) = %3D

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Q: Find the derivative of f(x) = 3x° cos(x). 8 CoS f'(x)

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

Q: Consider the function f(x) whose second derivative is f”(x) = 10x + 8sin(x) If f(0) = 2 and f’(0) =…

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Q: Consider the function f(x) whose second derivative is f”(x)=5x+2sin(x). If f(0)=4 and f’(0)=4, what…

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Q: Find y" by implicit differentiation. x² + 4y² = 4

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Q: Find the derivative of 2 cos x 1. f(x) x+1

A: As we know that: The Power rule: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2 Given: fx=2cosxx+1

Q: Consider the function f(x)  whose second derivative is f"(x) = 10x+4sin(x) . If f(0)=2  and f'(0)=3…

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Q: Compute the derivative of f(x) = 7 ln (x + 10) + In (x³ ): Answer: f'(x) =

A: Given function is  f(x)= 7ln(x+10) + ln(x3), we have to find the derivative of f(x) with respect to…

Q: The derivative of f(x) = 5x – Vx + (sin)x – e² -

A: Given; f(x)=5x4-x1/3+[sin(π/2)]x-e2

Q: Find  y''  by implicit differentiation. 4x2 + y2 = 4

A: Given,  4x2+y2=y,we have to find y''Differentiate with respect to x,we get…

Q: Find fifth order derivative of the function f(x) = x*Sin (2x +1) by using Leibnitz theorem.

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Q: 5) Find the second derivative of f (x) = %3D ex plify your answer as much as possible

A: fx=1-2xexTo find the second derivative

Q: Find the second derivative of f(x) = x2+ e* - COSX. O a. f(x) = 2x + xex - cosx O b. f'(x) = 2x + e*…

A: Solve by derivative

Q: Find sixth order derivative of the function f(x)=(x-5)^7.cos(5x) by using Leibnitz theorem.

A: n! = n × (n-1) × (n-2) × (n-3) × (n-4) × ............ × 1

Q: Consider the function f(x) whose second derivative is f''(x)=4x+3sin(x)   If f(0)=3  and f'(0)=2…

A: detailed solution with explanation is given below

Q: Compute the derivative: x4 – 4 d - at x = 2 dx x2 – 5 - The derivative is:

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Q: Find the second derivative of f(x) = sin(3x) - cos(2x)

A: We have to find second derivative of  f(x) = sin(3x) - cos(2x)  Then   First derivative of f(x) is…

Q: Find the derivative: 1+ e2x = cos 1 - e6x f(x) f'(x) =

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Q: Find y" by implicit differentiation x2 5y2 5 + = 2 X у"-

A: Take d/dx on both sides and distribute it on the left side. Derivative of constant =0

Q: Find the derivative of the logarithmic function. 3x f(x) = In %3D x+2,

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Q: Consider the function f(x) whose second derivative is f''(x)=8x+10sin(x). If f(0)=3 and f'(0)=2 what…

A: The function is f"x=8x+10sinx.   Integrate the function.…

Q: Find the derivative of f(x) = –4 ln (5 cos (-4x))

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Q: F(x) = "(5t - 1) dt %3D

A: We need to find the first derivative of F(x)=∫x2x(5t-1)dt. By Leibniz's integral rule,…

Q: Find the derivative of f(x) = 9 sinh-' (x²) – 9 In ( Vx4 + 1). %3D

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Q: Find the derivative of the function. f(x) 4. + 2cos x %3D

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Q: Find the derivative of the inverse function at x=1 for the function y=sin(x−1)+x2.

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Q: 4. F(x) = (1-t) dt

A: To find the first derivative

Q: Calculate differential: f(x) = e-* cos(3x) + 2 of the range [1,2] with h=0.05 Using the backward…

A: Equation is  f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of…

Q: Find the derivative of f (x) = arcsin (x²). 2x f' (x) = 1-a4 f' (x) V1-x4 2x O f' (x) = V1-a² O f'…

A: Use differentiation of trigonometric function

Q: Find the derivatives of inverse function: y = sec-1squareroot of 1 + x2 AND…

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Q: Find the derivative: f(x) = cos 1 + e8x 1- e6x – ebz f'(x) =

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Q: Consider the function f(x) whose second derivative is f''(x)=2x+3sin(x). If f(0)=2 and f'(0)=4, what…

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Q: Solve for the derivative of the Inverse Hyperbolic Differentiation. 1. y = sin h-1 (2x2 - 1) 2. y…

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Q: Find sixth order derivative of the function f(x) = (x – 5)7.cos(5x) by using %3D Leibnitz theorem.

A: If y=uv where, u and v are functions of x then un and vn denote the nth derivative of u and v with…

Q: Find the derivative of f(x) = ln v4 – x2 %3D

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Q: Compute the derivative for y= (e^-4x sin^2(x)) / (x^2 + 3x + 1)

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Q: Find the derivative of the function. 8 f(x) =x" log 6x .7 ,7 O A. X +8x log ,x .7 O B. In 6 + 8x log…

A: According to product rule of differentiation ddxuv=vddxu+uddxv and according to power rule of…

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

A: fx=11+x2 Differentiate the above function with respect to x. f'x=ddx11+x2=2x1+x22 Again,…

Q: Show that the derivative of f(x) =xln(x)−x is ln(x). Use this to compute∫ln(x)dx.

A: Sum/difference rule of differentiation,

Q: Find the derivative of f (x) = In(3x² – x)³ in two different ways; (a) with the chain rule %3D | and…

A: Given fx=ln3x2−x3aUsing Chain Rulelnfx'=1fxf'xDifferentiate w.r.t…

Q: Consider the function f(x) whose second derivative is f''(x)=2x+7sin(x). If f(0)=3 and f'(0)=3, what…

A: to find f'(x) integrate the given function c=integrating constant. Then plug x=0 and f'(0)=3 and…

Q: Find the derivative of f(x) = 3/x ln(x), f' (æ) =

A: Chufu