know what the derivative of e^(g(x)) is and what the derivative of In(g(x)) is. I.e. the chain rule for the exponential function f(x)=e^x and the chain rule for the natural log f(x)=In(x).

Q: Find f'(x) if f(x)=   and then simplify

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Q: Let X be exponential with mean 1/^; that is, fX(x) = λe^(-Ax), 01].

A: Let  be exponential distribution with mean .Its PDF is given by,Where,  is a parameter.

Q: Find the derivative and second derivative of g(x)=x(100-x^2)^(1/2).

A: Since the placement of the radical sign is not clear whether it includes x or no, the question has…

Q: Find the domain of this function: f(x) = e^x - e^-x

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Q: If f(x)=In(x-1), find the formula for f^((n))(x), the nth derivative of function f(x) f(x) = ln (x –…

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Q: Find F'(x) if F(x)= e^(-x^2) * x^(sin(x^3)) Use logarithmic differentiation

A: topic - logarithmic differentiation

Q: Find f''(x) if f(x) = e^3x^2+1.

A: calculate the second derivative for the given function

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: give the derivative of y = x^6

A: Solution-

Q: Use compositions to show that f(x)=7^(x) and g(x)=log_(7)x are inverses of each other.

A: Two functions f & g are inverses to each other by composition is (f∘g)(x)=x and (g∘f)(x)=x Here…

Q: Given that f(x)=2^(x)-1 and g(x)=log_(3)(x+5) determine the x value (s) where f(x)=g(x).

A: Given,  f(x)=2^(x)-1          g(x)=log_(3)(x+5)and f(x) = g(x)calculation of value of x are as…

Q: Find f(g(x)) if f(x)=e^(x) , g(x)=x^(2)

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Q: log_(3)(27^(x))/(9^(y)) can be written in the form px+qy. find p and q.

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Q: Find the derivative of f(x) = e-2 / x^2

A: Consider the function fx=e-2x2 Here, the objective is to find the derivative of the function.

Q: (a) Find the inverse of the function y = e? On the same diagram sketch the line y = x, and the…

A: We have to find the inverse of the given function.

Q: Evaluate the derivative of y=(cosh'(4x))* . Give your answer in natural logarithmic form.

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Q: Given f^(-1)(x)=log_((1)/(2))x, which of the following represents f(x) ?

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Q: Find the derivative of the logarithmic function. 3x f(x) = In %3D x+2,

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Q: find range of the following function log_(4)|x+(1)/(x)|

A: We have to find range of the given function.

Q: Let y = f(x) be the function. Use the definition of the logarithm to obtain the inverse functions x…

A: Solving

Q: Let m1 be the slope of the slope Y = 3ª at the point x = let m2 be the slope of the function y =…

A: topic - relation between slopes of curve

Q: If f(x) = log12(V3x* + x² + 4), find f'(x). Use exact values. f'(x) =

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Q: Suppose that f(x) = log (4x² + 1). Find f'(2). (Round your answer to four decimal places. f'(2) = X…

A: Topic = Derivative