2.4: Derivatives of Trigonometric Functions

We are interested in finding the derivative of trigonometric functions.

\[\dfrac{d}{dx} (\sin x) = \cos x \qquad \qquad \dfrac{d}{dx}(\cos x) = -\sin x\]

Trigonometric Functions

We can use the quotient rule to find derivatives of the trigonometric functions.

Differentiate the following:
  1. $f(x) = \tan(x)$
  2. $f(x) = \csc(x)$
An object hanging from a vertical spring is compressed upwards 4 centimeters from rest and released at $t = 0$. The position of the object at time $t$ is \[s = f(t) = 4\cos t\] Find the velocity and acceleration at time $t$.
Find the 27th derivative of $f(x) = \cos x$.