(a) Express the new function m(x) = ln in terms of the original function g(x) In(x). m(x) :

Q: find f'(x) of (((3x^2+1)e^x^2)/(2x+1)^5)^5 using logaithmic differentiation.

A: The given function is,

Q: Disprove the statement ln x / ln y = ln x - ln y,  by, a) Letting y equal a positive constant of…

A:

Q: then find f(x). | f(x)dx = = ln([x]) In(x) - sec(x) - 4e + 2 -x + 6x + C

A: The integration of f(x) equal to the;  ln(|x|)-sec(x)/3 -4ex/4+x2/2 +6x +C.

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

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

Q: 1. Find an equation of the tangent line to the graph of the function at the given point. f\xl=In…

A: Solved below

Q: Find the first derivative of each function. a) f(x)=ln (e^x+e^-x)

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Consider the function, f(x) = (x + 1)ln(5x² + e). Without finding explicitly the inverse of f(x),…

A: Given : fx = x+1ln5x2+e

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

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Q: Find the derivative of the function. y = In(e7x + 5)

A: Given y=ln(e7x+5)

Q: Find Find the second derivative of the given function. y = In(x² – 1)

A:

Q: (A) Find an equation of the tangent line to the graph of f(x)=(4x+1)sin(πx) at the point whose…

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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: (b) Sketch the graph of f (x) = ln(4 – x²). Use the first and second derivatives to identify where…

A: Consider the function  fx=ln4−x2

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: -e' 4. Y = e3x +e¬3X

A: Given: y=e3x-e-3xe3x+e-3x

Q: Find the derivative of this complex equation using logarithmic differentiation?

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Q: Find the finite derivative of a the functions below at x=1: a) f(x) = 4x³-3x²+2x-3 3 b) f(x)==-²/ 3…

A: Concept: The derivative can be represented as f'(x) or ddx(f(x)) Derivative of xn: ddx(xn)=nxn-1…

Q: Find the derivative of y with respect to the independent variable. x8)n 5) y =log 5 x-8

A: using the fact of logarithmic  logax=lnxln(a) find the derivative

Q: Find an equation of the tangent line to the graph of the function y = log10 2x, at the given point…

A: Given:y=log10 2x  through the given point 5, 1Equation of tangent line:y-y1=mx-x1Slope:dydx=f'x=m

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

A:

Q: 3. Find the derivative of the following using logarithmic differentiation: 2x a. y = (2x – 1)(x + 1)…

A: To find the derivative by using logarithmic differentiation first take  the  logarithm on  both…

Q: find the extreme values on the interval f (x) = x − 12 ln x, [5, 40]

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Q: 6. Find the derivative for each function. b. f(x) In 5x3 2)3 f(x) (e*3 2) а.

A: Use exponent rule for exponent 3 and use chain rule for (e^x^3 +2)

Q: Consider the function g(x) =2x³ - 6x+3. The critical values for this function are and since these…

A: We have to find critical points

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: Suppose h(x) = log (2 -;) What is the correct result of the derivative of h with respect to x? A…

A: use logarithm to find the derivative.

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

A: Solving the problem by finding the second derivative.

Q: 1. Find ALL THE DERIVATIVES of the function: f (x) = 2x7 – a5 + 5a³ – 8x + 4 2. Use logarithmic…

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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: 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: Q3: find the derivative of In(x4+3x-1) a) f(x) = %3D x²+1 b) f(x) = 4x³ . log(x² + 2x) %3D c) f(x) =…

A: Use product rule of differentiation.

Q: 9x Find the derivative of the function f(x)=In x2+15 2x O f'(x)= x²+15 15-x2 f"(x)= x2+15 2x O…

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Q: The derivative of the function f(x) = 5+ ln r is: 1 a. f'(x) = 2.x/5+ In x b. f'(x) = 2/5+ In x In x…

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Q: Find the derivative of y. x2 =log6 x+1 O A) Sx+1 x2 O B) ) In 6 x2 2x+1 1 Sx+1 In 6 x2 D) None of…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. Find the derivative of the following (a) f(x) = log-(r* +2) + 7** (b) k(r) = In(x) + 5e¯ (c) j(z)…

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

A: Given function is,

Q: 15) Determine the 3rd derivative of the function f(x) = 2\x-x³ [T:2]

A: topic - derivatives

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 function. h(x) = ln(2x2 + 1)

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Q: Consider the function g defined by 1 g(x, y) = cos (7x/) - CoS log3(x – y)

A: Given problem:-

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

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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: x² +2x+1 6.) f(x) = 3

A: The given function is f(x)=x2+2x+13. Find the first derivative or f'x of the functions by using the…

Q: 1- Find the first derivative of y with respect to x for the following functions: In5 7x y = log5 . a…

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Q: 7. Find the second derivative of the following function: y = e** +In(7e¯* + 5x³) – 5²× +-

A: