Rebekah Hahn

2023-03-08

Find the second derivative of the following function: $y={e}^{3x+2}$
A. ${e}^{3x+2}$
B. ${e}^{9y}$
C. $3{e}^{3x+2}$
D. $9y$

Valentino Sloan

We have,
$y={e}^{3x+2}$
We must employ the chain rule in order to distinguish this function.
First derivative of this function is:
$\frac{dy}{dx}={e}^{3x+2}.\frac{d}{dx}\left(3x+2\right)$
$\frac{dy}{dx}=3{e}^{3x+2}=3y$
Second derivative of this function is:
$\frac{{d}^{2}y}{d{x}^{2}}=\frac{d}{dx}3{e}^{3x+2}=3y.\frac{d}{dx}\left(3x+2\right)$
$\frac{{d}^{2}y}{d{x}^{2}}=9y$

Do you have a similar question?