Question

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

Answer 1

Answer:

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

Step-by-step 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:

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

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

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