Question

Find the derivative:
f(x)=tan(x^2+5)

Answer 1

`f'(x)=2x \sec^2(x^2+5)`

Explanation:

To differentiate this we will need to use the chain rule:

`[h(g(x))]'=g'(x) \cdot h'(g(x))`.

We will also have to keep in mind how to differentiate the following:

`\tan(\theta)` with repect to
`\theta`

`x^2+5` with respect to
`x`.

`f(x)=\tan(x^2+5)`

Derivative of both sides:

`f'(x)=(x^2+5)'\cdot (\tan)'(x^2+5)`

`f'(x)=(2x+0) \cdot \sec^2(x^2+5)`

`f'(x)=2x \sec^2(x^2+5)`