Determine the equation of the tangent line to the graph of y = f'(x) at the point where x = 1 if f(x) = log10(a³ +1).

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

A:

Q: Find the derivative of f(x) = COS 4 log3 (x²) os(5x)

A: Explanation of the answer is as follows

Q: Find the derivative of the function. f(x) = In(sinh(x)) f '(x) =

A: f(x) = ln(sinh(x)) here we use chain rule f'(x) = cosh(x)/sinh(x) f'(x) = cot(h(x))

Q: Find the derivative of function.

A: To find the derivative of the given function                                                y=log…

Q: Find the nth-order derivative of the function y=arctanx at the point x=0.

A:

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

A:

Q: L(x) = In(x)+log,(x)

A: Used formulas : ddx(logax) = 1x ln a ln x = loge xloge e = ln e = 1ln 5 =1.61

Q: Find the derivative of y with respect to the given independent variable. y= 0 sin (log 50)

A: Given problem is, y=θsinlog5θ we have to  differentiate it with respect to θ.

Q: Find the derivative, if y3 (log x)* + y = (log x)* +(sinx) -1

A:

Q: Compute the derivative in terms of log for y=log(xe^(-3x))

A:

Q: find the derivative of y with respect to the givenindependent variable. y = θ sin (log7 θ)

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Q: What is the first derivative of s(x)=(6x)^3x at x=3? Enter an exact answer in terms of a natural…

A: We will take the logarithm with base e and then find the derivative with respect to x and then…

Q: Determine the percentage relative error (In 2 decimal places) when we compare the derivative of…

A:

Q: Compute for the derivative of the function using logarithmic differentiation g(y) =…

A: Logarithmic differentiation: - The use of logarithms to derive the derivatives of some difficult…

Q: Calculate the derivative at the point (1,1) of the function given by the equation x−y=ln(xy) where…

A:

Q: Find the derivative with respect to t. y= csc-1(et)

A: Given:

Q: find an equation of the tangent line at the point indicated. y = log2(1 + 4x−1), x = 4

A: We have to find an equation of the tangent line at the point indicated. the given function is…

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

A:

Q: find the derivative of y with respect to the appropriatevariable. y = sinh-1 √x

A: Find the derivative of y with respect to the appropriate variable.

Q: Find an equation of the tangent line to the graph of the function at the given point.

A: Here given function as y=log102xory=log 2xlog 10 Differentiate with respect to x dydx=log2xlog…

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

A:

Q: calculate the derivative with respect to x. ln x + ln y = x − y

A:

Q: Find the derivative of ,In sin-1) y = e %3D

A:

Q: Find the derivative of the function f(x) = 5ª+x² + log3 (In x). %3D

A: To find the derivative of the given function.

Q: Calculate the derivative. 1 y = log 5x y' =0

A:

Q: Find the derivative of the function f(x.y) = tan -1 y at the point (4, - 4) in the direction in…

A:

Q: 3x g(x)=e* In(4x+1) (с)

A:

Q: = Determine the equation of the tangent line to the graph of f(x) = I x+ln x cosh (√2t - 1) dt at x…

A:

Q: What is the first derivative of the expression (xy)× = e?

A: See the details solution in below

Q: find the derivative of y with respect to the givenindependent variable. y = 3 log8 (log2 t)

A:

Q: Find the derivative of the function. y= log 4- x

A:

Q: Determine the derivative: y = log (3x2) (01)प य log (3) ** In(10) 6 log (Sx) r In(10) Oy= 18x In(10)…

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Q: Find an equation of the tangent line to the graph of the logarithmic function at the point (1, 0). y…

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Q: Find a number such that the tangent line to the graph y= log,(x) at x = a is parallel to the tangent…

A: The objective is to find the value of a

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 derivative of y with respect to the given independent variable y= 0 sin (log 50)

A: Given that, y=θsinlog5θ

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 y with respect to the givenindependent variable. y = log2 5θ

A:

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

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: f y = (sin x)x b

A:

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

A: On simplification, we get

Q: Find the derivative of f(x) = log(-6x* – 6x + 5) at the point x = 2. Provide your answer below:…

A:

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…

Q: Find the second derivative of y=x-1 at x=2

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Q: 2. Calculate the derivative of y = arccos(e arcsin(x2)

A: Let u=arcacos(e^x) and v=arcsin(x^2), then y=u/v

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

A:

Q: Determine the equation of the tangent line to •x³ +ln x the graph of f(x) at x = 1. [² = √/3 + 5t5dt

A:

Q: Find the equation of the tangent line to the curve y = log(x2-3x+1) at the point (3,0)

A: