Differentiate y = e^x (1 + x)

We will use the concept of differentiation in order to find the value of dy / dx.

Answer: Differentiation of y = e^x (1 + x) is dy / dx = e^x (2 + x)

Let us see how we will use the concept of differentiation in order to find the value of dy / dx.

Explanation:

The function that is given to us is y = e^x (1 + x)

The function can also be written as y = e^x + e^x x

On differentiating both sides using product rule of differentiation we get,

dy / dx = d ( e^x ) / dx + d ( e^x x ) / dx

= e^x + e^x dx / dx + x d (e^x ) / dx

= e^x + e^x + x e^x 

= 2e^x + xe^x

= e^x (2 + x)

Hence, for the given function y = e^x (1 + x), dy / dx = e^x (2 + x).