3. Techniques of Differentiation

5–24. For each of the following composite functions, find an inner function u=g(x) and an outer function y=f(u) such that y=f(g(x)). Then calculate dy/dx.

y = (5x²+11x)^4/3

5–24. For each of the following composite functions, find an inner function u=g(x) and an outer function y=f(u) such that y=f(g(x)). Then calculate dy/dx.

y = sin⁵x

5–24. For each of the following composite functions, find an inner function u=g(x) and an outer function y=f(u) such that y=f(g(x)). Then calculate dy/dx.

y = sin x⁵

5–24. For each of the following composite functions, find an inner function u=g(x) and an outer function y=f(u) such that y=f(g(x)). Then calculate dy/dx.

y = √x²+1

Calculate the derivative of the following functions.

y = cos⁴ θ + sin⁴ θ

Calculate the derivative of the following functions.

y = (2x⁶ - 3x³ + 3)²⁵

Calculate the derivative of the following functions.

y = (1 + 2 tan u)^4.5

Calculate the derivative of the following functions.

g(x) = x / e^3x

Calculate the derivative of the following functions.

y = sin(sin(e^x))

Calculate the derivative of the following functions.

y = cos^7/4(4x³)

Calculate the derivative of the following functions.

y = (1 - e^0.05x)^-1

5–24. For each of the following composite functions, find an inner function u=g(x) and an outer function y=f(u) such that y=f(g(x)). Then calculate dy/dx.

y = √7x-1

5–24. For each of the following composite functions, find an inner function u=g(x) and an outer function y=f(u) such that y=f(g(x)). Then calculate dy/dx.

y = e^4x²+1

5–24. For each of the following composite functions, find an inner function u=g(x) and an outer function y=f(u) such that y=f(g(x)). Then calculate dy/dx.

y = e^√x

5–24. For each of the following composite functions, find an inner function u=g(x) and an outer function y=f(u) such that y=f(g(x)). Then calculate dy/dx.

y = tan 5x²