6. Derivatives of Inverse, Exponential, & Logarithmic Functions

In Exercises 57–70, use logarithmic differentiation to find the derivative of y with respect to the given independent variable.

64. y = 1/(t(t+1)(t+2))

In Exercises 25–30, use logarithmic differentiation to find the derivative of y with respect to the appropriate variable.

27. y = (((t+1)(t-1))/((t-2)(t+3)))^5, t>2

In Exercises 115–126, use logarithmic differentiation or the method in Example 6 to find the derivative of y with respect to the given independent variable.

115. y = (x + 1)ˣ

75–86. Logarithmic differentiation Use logarithmic differentiation to evaluate f'(x).

f(x) = (1+x²)^sin x

75–86. Logarithmic differentiation Use logarithmic differentiation to evaluate f'(x).

f(x) = x^10x

49–55. Derivatives of tower functions (or g^h) Find the derivative of each function and evaluate the derivative at the given value of a.

f (x) = (4 sin x+2)^cos x; a = π

In Exercises 115–126, use logarithmic differentiation or the method in Example 6 to find the derivative of y with respect to the given independent variable.

126. eʸ = y^(ln x)