# If f(x)= tan8 x  and g(x) = e^(5x ) , how do you differentiate f(g(x))  using the chain rule?

Mar 31, 2016

$f \left(g \left(x\right)\right) = 40 {e}^{5 x} {\sec}^{2} \left(8 {e}^{5 x}\right)$

#### Explanation:

As $f \left(x\right) = \tan 8 x$ and $g \left(x\right) = {e}^{5 x}$

$f \left(g \left(x\right)\right) = \tan \left(8 {e}^{5 x}\right)$

and $\frac{\mathrm{df}}{\mathrm{dx}} = \frac{d \left(\tan 8 {e}^{5 x}\right)}{d \left(8 {e}^{5 x}\right)} \cdot \frac{d \left(8 {e}^{5 x}\right)}{\mathrm{dx}}$

= ${\sec}^{2} \left(8 {e}^{5 x}\right) \cdot 8 \cdot {e}^{5 x} \cdot 5$

= $40 {e}^{5 x} {\sec}^{2} \left(8 {e}^{5 x}\right)$