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

Q: Determine the first derivative of the ff. function y = tan(ln(cot(x² + 3 ln 3x)))

A: Chain rule of differentiation: f(g(x))'=f'(g(x))g'(x) Formulae used: ddxtanx=sec2xddxlnx =1xddxcot…

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: 10. Find the first derivative: f(x) = (x³ + 2x) In x

A: Given Data: Function: fx=x3+2xlnx The product rule of derivative is, ddxfx·gx=fxddxgx+gxddxfx Use…

Q: In y = 22 cosh1 2x

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

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Q: Find the derivative of sinh(x)tanh(x).

A: As per our guidelines I am solving only first problem please repost other question.  y = sinh(x).…

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

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Q: Solve for the derivative of the Hyperbolic Differentiation. 1. y = ex cos h 2x 2. y = ln sin h x…

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Q: What is the first derivative of q(x)= ln((7x^2+3x+7)/((x^5/6)(tan(x)))

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Q: 12) Find the first derivative of f(x) = 3x %3D

A: Use rules of derivative

Q: 11 In(x)sin (x²). Find the first derivative of g(x) (x),6

A: As we know that: The product rule: f·g'=f'·g+f·g' The chain rule: fgx'=f'gx·g'x The Power law:…

Q: 4. Find the derivative of g(x) = e5" sin(-x). Do not simplify.

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Q: Compute the derivative of the function y=x2/ln x at x=e.

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Q: 4. Find an equation of the tangent line to the graph of f(x) = ln(x ^2 + 4) at the point (2, ln(8))

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Q: Find the derivative: y = 6 In x 6 ln x-1 x7 1-6 ln x 12 1+6 ln x x12 4 O 1-6 ln x x7 O

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Q: 26 Find the 155th derivative of (1 + x°)" at x = 0.

A: see 2nd step.

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 the following function. y= 4 ln x – In(x-8)

A: we have to derivative

Q: 1 14) Use the definition of derivative to find dx 3- х.

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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: find the derivative of y with respect to the appropriate variable.23. y = (x2 + 1)sech (ln x)

A: Definition used -             ddxsech(x) = -tanhxsechx          Product rule of derivative -…

Q: 3// By using logarithmic differentiation and with respect to independent variable x, find the…

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Q: Find the derivative of  y=ln [tan-1(7x5)] with respect to x.

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Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = x4/4 ln x - x4/16

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Q: 22 Find the 43rd derivative of (1 + x²)“ at x = 0. 0.

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

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Q: What is the derivative of: y = ln ln(1 − cos x)

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

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Q: 7. Find the nth derivative of y = 1//x.

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

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

A: Given:

Q: The derivative of y = -ln(cos(ex + 1)) is

A: Our Aim is to find the derivative of y=- ln cos ex+1 -(i)

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

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Q: find the derivative of y with respect to the givenindependent variable. y = log4 x + log4 x2

A: Given: By using logarithm base change rule, the function can be rewritten as follows,

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 y, below. 9x(ln x + In 2) – 8x + v2 %3D

A: first, simplify the function  y=9xlnx+ln2-8x+2 y=9xlnx·2-8x+2 y=9xln2x-8x+2

Q: 10. Find the first derivative: f(x) = (x³ + 2x) In x %3D

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Q: Find the derivative. 8 + e y = In 8 + et 8 - ex.

A: Given,          y=ln8+ex8-ex

Q: 19. Find the derivative of 16 = xy using implicit differentiation.

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Q: 3. Find the second derivative using implicit differentiation x² + y? = 4

A: Given that x2+y2=4To find implicit differentiation

Q: 4) Find the derivative of y = arctan(x² + 3)

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Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

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Q: Find the first derivative of y = cos*x- sin*x.

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Q: 3. Find the derivative of: y = csch¬(In (sech(sec()))).

A: Note:Two questions submitted simultaneously, kindly upload question 2 separately.

Q: (x² +SJ° In 14-X つ. dr

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Q: Find the derivative of the function 3- y = e- sin 3x 4- y csc- (x2 + 1)

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Q: 2. Find the derivative In (x+) y3=

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Q: 8. Find the derivative of y = In(3t) dt.

A: To Determine: Find the derivative of given integral:…

Q: 8) Find the first derivative of f (x) = sin 2 (x3).

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Q: find the derivative of y with respect to the givenindependent variable. y = log3 (1 + θ ln 3)

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Q: Find the derivative of V(x) = ln(sin x) – (x4 – 3x)10

A: We can find the derivative as below.