Question

Find the second derivative of the following function: $y=e^{9x+15}$

• A. $81y$
• B. $e^{9y}$
• C. $9e^{9x+15}$
• D. $e^{9x+15}$

Answer 1

The correct option is A $81y$

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

First derivative of this function is:
$\frac{dy}{dx}=e^{9x+15}.\frac{d}{dx}(9x+15)$
$\frac{dy}{dx}=9e^{9x+15}=9y$

Second derivative of this function is:
$\frac{d^{2}y}{d{x}^2}=\frac{d}{dx}9e^{9x+15}=9y.\frac{d}{dx}(9x+15)$
$\frac{d^{2}y}{d{x}^2}=81y$