Let h(x)=f(x)g(x), where f(x)=ln(4x2−3x) and g(x)=3x−1. What is h′(x)?

Q: Find the differential of the function. Y = e2x

A: Given function is  y= e2x

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

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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: Compute the indicated derivative. d + 7x)(x2. dx x = 2

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Q: Suppose that f(x) = 11x – 4 ln(x), x > 0.

A: (g) Find the double derivative for f(x).…

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Q: Find dx * for y = (x² + 2)°(1 – x³)* using logarithmic differentiation.

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Q: Use the u-substitution to find the anti-derivative of m'(x)= 1/xln(x)

A: solution :- antiderivative is the integration  So put ln(x)  = u Then (1/x )dx  = du And then…

Q: What is the value of ln[f'(2)] if f(x) = e^x?

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Q: Find the first derivative of the function g(x) = V5 +x +4cos (2x).

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: Find the derivative of the function f(x) = ln(e" + 5).

A: We have to find the derivative of the function -          f(x)=ln(ex+5) Here , we will use the…

Q: Find the derivative y = (2x – a) (x² + e-")

A: We havey= (2x-x3)(x2 + e-x)

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

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Q: Find the second derivative. 1 h(x) = x2 %3D | h"(x) = %3D

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Q: S-2(x-1 - x²) dx 5.

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Q: Find the first derivative of: x = t²e2t

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

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

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Q: 3 Find the first derivative of f (x) = 3x e

A: Given that : f(x)= x3 / e3x. Find the first derivative of this function. We know that d(xn)/dx =…

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: Q. / Find the derivative of y = (In(x²))'n(x²).

A:

Q: 9. Find the derivative of y = xe3-x (A)e3-x? (B) 0 (C) e³-x*(1– 2x?) (D)–2xe³-x² (E) e3-x*(1+ 2x²)

A: Given : y = xe3-x2

Q: Find the second derivative of the function. g(x) = 9/x + e6× In(x) g"(x) = %3D

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Q: Find the derivative of the composite natural exponential functions 1. f(x) = In x² x-2 2. g(x) =…

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Q: h(x) = (cos x)(4x²– 3)

A: Explanation of the answer is as follows

Q: 1. Find the anti-derivative of the following. e" (x + 1) dx x2

A: From the given information. Anti-derivative has to be calculated to the following expression.

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

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Q: e2x -e-2x e2x+e-2x

A: Solving the problem by finding the second derivative.

Q: Determine the function f satisfying the differential equation f'(x) = xe-f(x) and f(0) = ln(2) =…

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Q: 4) Find the derivative of each function. a. f (x) = In(x² – 4) In e c. f (x) = b. f (x) = x² ln x

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Q: h(x) = In (2x-2)+(x² +1)e³x-6 %D Calculate the derivative at x=2, that is h'(2)=

A: calculate the derivative as shown below: h'x=ddxln2x-2+x2+1e3x-6…

Q: Find the second differential of the function y=x2cos2x.

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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: 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: Find the slope of the tangent line to the exponential function at the point (0, 1). y 2 1 (0, 1) -2…

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Q: 2x Find the derivative of h(x) 2x + 3

A: Given:  Function  h(x)=-2x2x+32

Q: Find the first derivatives of y = x3 – x + 2 e*

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

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Q: Differentiate the function g(x) = ln(xe-2x).

A: Given function is,

Q: Find the derivative of f(x)=

A: We use the quotient rule of logarithm to simplify the expression

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

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Q: Find the derivative of the given function e5x (2x+1)5 b. f(x) = In Vx²+1 f(x) = (x In x – x)

A: Given that: b. f(x)=lne5x(2x+1)5x2+1c. f(x)=(xlnx-x)

Q: Find the derivative of the function. h(x) = ln(2x2 + 1)

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Q: nd the derivative of the function  h(x)=ln(4x^2+3)

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Q: Find the anti-derivative of g'(x)= log1/2(X)

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Q: Find the derivative of the exponential function f ( x ) = 5x 2 e 7x

A: Given function: f(x)=5 x2 e7x     Calculate the derivative of f(x): f(x)=5 x2 e7x   Take the…

Q: Find the derivative of the given function. e5x (2x+1)5 f(x) = In Vx2+1

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Q: Given g(x) = ln(11x³ + x), the derivative s! (x)f 3x2 11x° + x 33x2 + 1 33x2 + 1 11x³ + x 33x2 +1 O…

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Q: Find the derivative of the function f(x) below. f(x)=ln(5−e^(−4x)) f′(x)=

A: Explanation: Given that, f(x)=ln(5-e-4x) Differentiate both sides with respect to x.…