Question

Find the second derivative of the following function: $y=e^{3x+2}$

• A. $9y$
• B. $e^{9y}$
• C. $3e^{3x+2}$
• D. $e^{3x+2}$

Answer 1

The correct option is A $9y$

We have,
$y=e^{3x+2}$
To differentiate this function, we need to use chain rule.

First derivative of this function is:
$\frac{dy}{dx}=e^{3x+2}.\frac{d}{dx}(3x+2)$
$\frac{dy}{dx}=3e^{3x+2}=3y$

Second derivative of this function is:
$\frac{d^{2}y}{d{x}^2}=\frac{d}{dx}3e^{3x+2}=3y.\frac{d}{dx}(3x+2)$
$\frac{d^{2}y}{d{x}^2}=9y$