Ramsey

2021-10-07

Find derivatives of the functions defined as follows: $y={7}^{3x+1}$

Alannej

Step 1
$y={7}^{3x+1}$
or
$y={7}^{3x}\cdot 7$
or
$y=7\cdot {7}^{3x}$
Use formula of derivative
$\frac{d}{dx}\left({a}^{x}\right)={a}^{x}\mathrm{ln}a$
Step 2
Differentiate y with respect to x
$\frac{dy}{dx}=\frac{d}{dx}\left(7\cdot {7}^{3x}\right)$
$=7\frac{d}{dx}\left({7}^{3x}\right)$
$=21\cdot {7}^{3x}\mathrm{ln}7$

Jeffrey Jordon