# How do you find the derivative of y=tanh(6+e^(6x))?

Jun 28, 2016

Simple application of the chain rule.

#### Explanation:

$\frac{d}{\mathrm{du}} \left(\tanh \left(u\right)\right) = {\sech}^{2} \left(u\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{du}} \cdot \frac{\mathrm{du}}{\mathrm{dx}}$

So ${\sech}^{2} \left(6 + {e}^{6 x}\right) \cdot \frac{d}{\mathrm{dx}} \left(6 + {e}^{6 x}\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 6 \cdot {e}^{6 x} \cdot {\sech}^{2} \left(6 + {e}^{6 x}\right)$