3. Techniques of Differentiation

Find the derivative of the function.

$f\left(x\right)=\sin \left(3x^2\right)$

Find the derivative of the function.

$y=3{\cos }^4\theta$

Find the derivative of the function.

$f\left(t\right)=\sec (4t+5)$

Find the derivative of the function.

$f(x)=\sin^5(2x^3+1)$

Find the derivative of the function.

$y=\cos^3\left(\sec\theta\right)$

Calculate the derivative of the following functions.

y = sec(3x+1)

Calculate the derivative of the following functions.

y = tan e^x

Calculate the derivative of the following functions.

y = sin (4x³ + 3x +1)

Calculate the derivative of the following functions.

y = csc (t² + t)

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