Givenf (x) = ln x, what is the derivative function f' (x), and what is its domain? f' (æ) = e², for all æ + 0 • f' (x) = ;, x > 0

Q: Find the derivative of the function.   f(x) = x5 ln(x)   f'(x)=

A: We have to find the derivative of function: fx=x5lnx Here there are two function in multiplication…

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y= ln x3

A: Given:

Q: Find the derivative of the function.…

A: The given function is hx=x2arctan8x

Q: Find the second derivative for the functions defined as follows g(x) = 4x(ln x)

A: We have to find second derivative of the function: gx=4x lnx Since two function are in product so we…

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

A: Use derivative formula :- f(x) = lnx then derivative f'(x) =1/x

Q: Find the derivative of f(x)=ln(x^3-x+2)

A:

Q: Find the derivative of function. y = ln(2 - 5x)

A: we have to find the derivative of y = ln(2 - 5x)

Q: Find the derivative. h(x) = In(cosh(7x)) h'(x) =

A:

Q: By using logarithmic differentiation and with respect to independent variable x, find the derivative…

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Q: Find the derivative of k(x) = log3(x) cos

A:

Q: Find the first derivative of y = (ln x)4

A: Given the  y = ( ln x)^4 We need to find the first derivative . Therefore differentiate to given…

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: y = In- e 2x+1

A:

Q: Find the first and second derivative of any function defined implicitly by yx2+ y2= x

A: Given,           yx2+y2=x

Q: In the given question as follows, find the derivative of the function.   y = ln(2 - e5x)

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Q: f (x) = ln(x · 5*)

A:

Q: y = x*(1 – In x4)

A:

Q: If C(x)=x' + x°, evaluate the fourth derivative at x = 2. %3D

A: To find the fourth derivative of the function: C(x)=x5+x-3 at x=2

Q: 8. Find the derivative of the function. y= In(1+x)

A:

Q: Find the derivative of the function. h(x) = x² arctan(5x) h'(x) =

A: h(x)=x2tan-1(x)

Q: find the first and second derivatives of f(x) = ln (x+1)

A: f'(x)=1x+1 and  f''(x)=-1(x+1)2

Q: 3) Find the first derivative of y=(In x)"

A: According to our guideline 3 subparts of question or the first question can be answered and rest of…

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (x2 ln x)4

A:

Q: Find the derivative of the following function. y= 4 ln x – In(x-8)

A: we have to derivative

Q: Find the derivative of n^(ln⁡(cosu)). Where n=822

A: Given information : nlncosu Here, n=822. we have to find the derivative of given function.

Q: a the derivative of h(x) = ln + 2 x5 et |

A:

Q: Find the derivative of the function. f(x) = x6 ln(x)

A:

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (θ + 1) - eθ

A:

Q: Find the derivative of the function  f(x)= e^-3x ln x

A: Given function is

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = 1/ln 3x

A: Given:

Q: Find the derivative of the function. f(x) = ln(x2 + 3)

A:

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln3/x

A:

Q: Find the equation of the tangent line to the graph of f(x) = 4^(x/ln2) at the point where x is ln16.

A: We find dy/dx to find the slope at x.

Q: Find the derivative of the function. f(x) = ln(4x)   f '(x) =

A: Given function

Q: Find the derivative of the function - 3x f(x) = 3 ln(x) + e - df dx

A:

Q: Find the derivative of the function g(x) = ln √2x

A:

Q: find the derivative of y with respect to the givenindependent variable. y = log2 (8tln 2)

A: We first expand the equation using the addition property of log and the change of base property.

Q: Find the derivative of g(x) = e-" cos(x²)

A:

Q: What is the first derivative of g(x) = ln #*+1? x2

A: Derivative of ln(x):       ddx(ln(x))=1x Division rule of derivative:-…

Q: What is the derivative of e^-x

A: Given query is to find derivative of e-x

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (sec (ln θ))

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Q: is the derivative of In

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Q: Shows the derivative function of: x³  + ln x(3x² + 5)

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Q: Calculate the derivative of the function y=log2 x ln (2x) at x=1.

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Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (ln x)

A:

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: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln 3x + x

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Q: Find the derivative of f(x) = x/ln (x)

A:

Q: Find the derivative of the function y = ln 5x/(1 − x)

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