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. $9y$

A. ${e}^{3x+2}$

B. ${e}^{9y}$

C. $3{e}^{3x+2}$

D. $9y$

Valentino Sloan

Beginner2023-03-09Added 3 answers

We have,

$y={e}^{3x+2}$

We must employ the chain rule in order to distinguish this function.

First derivative of this function is:

$\frac{dy}{dx}={e}^{3x+2}.\frac{d}{dx}(3x+2)$

$\frac{dy}{dx}=3{e}^{3x+2}=3y$

Second derivative of this function is:

$\frac{{d}^{2}y}{d{x}^{2}}=\frac{d}{dx}3{e}^{3x+2}=3y.\frac{d}{dx}(3x+2)$

$\frac{{d}^{2}y}{d{x}^{2}}=9y$

$y={e}^{3x+2}$

We must employ the chain rule in order to distinguish this function.

First derivative of this function is:

$\frac{dy}{dx}={e}^{3x+2}.\frac{d}{dx}(3x+2)$

$\frac{dy}{dx}=3{e}^{3x+2}=3y$

Second derivative of this function is:

$\frac{{d}^{2}y}{d{x}^{2}}=\frac{d}{dx}3{e}^{3x+2}=3y.\frac{d}{dx}(3x+2)$

$\frac{{d}^{2}y}{d{x}^{2}}=9y$