Calculate the implicit second derivative of b(z)=(x-5)^2 find the value of b''(-1

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 derivative of the logarithmic functions: y = ln (tan^2 θ )

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Q: find the derivative of - (z+j)?

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Q: Shows the derivative function of: 2x² + ln x²(2x² + 5x − 1)

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Q: What is the derivative of ex? What does it mean that the derivative is equal to the value of the…

A: Explanation of the solution is given below...

Q: 4. By implicit differentiation , find the 1st derivative of x3 + y3 + 6xy = 0

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Q: 29. Find the 5th derivative ofy= sin2x

A: 29. Given function is, y=sin2x. The first derivative of y is, y'=ddxsin2x=cos2x·2=2cos2x   The…

Q: find the derivative of y with respect to the givenindependent variable.

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Q: find the derivative of the function  y'=ln(squared root of x^2-4) and  y=ln IsinxI

A: The given function is y=lnx2-4. Obtain the derivative as follows.…

Q: On which derivative rule is the Substitution Rule based?

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Q: 2.) Find 1st derivative of y = e-'In (x-1)

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Q: 5) Find the derivative using logarithmic differentiation: y = Xcanx

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: 2. Use logarithmic differentiation to find first derivative of y (sinx)r

A: Formula used: ddx[u(x)v(x)]= u(x)v(x).ddx[ln(u(x)).v(x)] ddx(u.v) =dudx.v + udvdx

Q: 2. Use logarithmic differentiation to find first derivative of y = (sinx)*

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Q: Solve for the derivative of the function using chain rule. 11. f(x)= ln(sin(8x))

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Q: Evaluate the 2nd derivative at the given point.

A: We differentiate both sides with respect to x. Then we plug the given point.

Q: y = In (csc 2)

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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 function.

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Q: Find the derivative of xn by first principle or ab-initio method.

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Q: Find 1st and 2nd derivative of:   f(x)=(5x^4 + 3x^2)*ln(x^2)

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Q: FInd the derivative of f(x) =ln 1+ex/1-ex

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Q: Find the derivative of ry = -3+x*y° using implicit differentiation.

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Q: Find the second derivative using implicit differentiation of the given xì + yi = a

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Q: Find the function ƒ(x) whose derivative is sin x and whose graph passes through the point (0, 2).

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Q: Find the derivative of y with respect to the appropriate variable. y = cosh12 x+ 5

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Q: Calculate the derivative of y = e1+sinx.

A: Given, y = e1+sinx.

Q: Solve for the derivative of the function using chain rule. 7. f(x)= sin(e3x)

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Q: Find the first and second derivative of f(x) = ln(x)/rootX

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

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Q: find the derivative of y with respect to the givenindependent variable. y = log25 ex - log5 √x

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Q: Compute the derivative of (ln x)^ln x

A: To find the derivative of (ln x)ln x Using the exponent rule ab=eb ln a we get, (ln x)ln x=e(ln x)ln…

Q: Find the derivative of ƒ(z) = ln2x 1. 2z

A: We first expand using the addition property of log.

Q: Calculate the third derivative of the function y%-xe-",

A: To find the third order derivative we use product rule of derivative formula. From the product rule…

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

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Q: Use Delta method to find the derivative of e*

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Q: Find the derivative of the function without using the Quotient Rule. y = -

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Q: Find the derivative of (ex + e-x )/(ex - e-x )

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Q: Find the 1st derivative of y= Arcsin x -v -V1-x²

A: To find the first derivative of y = sin-1x - 1-x2 sin y =x - 1-x2

Q: is the derivative of In

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

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Q: In(x-

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Q: Compute the derivative of the given function. f (x) = 2 ln x – vT

A: Given fx=2lnx-x To find the derivative:

Q: What is the derivative of the function  x^8(ln(x))?

A: To find the derivative of the function x8(ln(x)) as follows.Redefine the function as follows.

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

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Q: Find and sketch an exponential equation of the form y = Cekx that passes through the points (0, 8)…

A: Given an exponential equation of the form y=Cekx that passes through the points (0,8) and (3,4). To…