3. Techniques of Differentiation

Calculate the derivative of the following functions.

y = ⁴√(2x / (4x - 3))

What is the derivative of y = e^kx?

Find f′(x) if f(x) = 15e^3x.

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 = (3x+7)¹⁰

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