Question

Find d2y / dx2 if y = enx

Answer 1

y=e^nx

dy/dx= ne^nx

d²y/dx²=n²e^nx

y''=n²y

Answer 2

Answer:

$\bf \frac{d^2y}{dx^2}=n^2\cdot e^{nx}$

Step-by-step explanation:

$\text{Let y = }e^{nx}$

We need to calculate the double derivative of y. So, in order to find double derivative of y we first need to find the first derivative of y by differentiating y with respect to x :

$\frac{dy}{dx}=e^{nx}\times \frac{d}{dx}(nx)\\\\\implies \frac{dy}{dx}=n\cdot e^{nx}$

Now, to find double derivative of y, Again differentiate the obtained first derivative of y with respect to x

$\frac{d^2y}{dx^2}=n\cdot e^{nx}\times \frac{d}{dx}(nx)\\\\\implies \frac{dy}{dx}=n^2\cdot e^{nx}$

$\bf Hence, \frac{d^2y}{dx^2}=n^2\cdot e^{nx}$