Question

Differentiate the following w.r.t. x :

Answer 1

Given expression is e x + e x 2 +...+ e x 5 .

Let the expression be y= e x + e x 2 +...+ e x 5 .

Now, differentiate the expression on both the sides with respect to x.

dy dx = d( e x + e x 2 +...+ e x 5 ) dx = d( e x ) dx + d( e x 2 ) dx + d( e x 3 ) dx + d( e x 4 ) dx + d( e x 5 ) dx = e x + e x 2 ⋅ d( x 2 ) dx + e x 3 d( x 3 ) dx + e x 4 d( x 4 ) dx + e x 5 d( x 5 ) dx = e x +2x e x 2 +3 x 2 e x 3 +4 x 3 e x 4 +5 x 4 e x 5