$e^{x} + e^{x^{2}} + . . . + e^{x^{5}}$ differentiate w.r.t $x$

Open in App

Solution

Let
$y = e^{x} + e^{x^{2}} + . . . . . . . + e^{x^{5}}$

$\frac{d y}{d x} = \frac{d (e^{x} + e^{x^{2}} + . . . . . . e^{x^{5}})}{d x}$

$= \frac{d e^{x}}{d x} + \frac{d (e^{x^{2}})}{d x} + \frac{d (e^{x^{3}})}{d x} + \frac{d (e^{x^{4}})}{d x} + \frac{d (e^{x^{5}})}{d x}$

$= e^{x} + e^{x^{2}} \frac{d x^{2}}{d x} + e^{x^{3}} \frac{d x^{3}}{d x} + e^{x^{4}} \frac{d x^{4}}{d x} + e^{x^{5}} \frac{d x^{5}}{d x}$

$= e^{x} + 2 x e^{x^{2}} + 3 x^{2} e^{x^{3}} + 4 x^{3} e^{x^{4}} + 5 x^{4} e^{x^{5}}$

Suggest Corrections

Similar questions

x

y = e^{x} + e^{x^{2}} + . . . + e^{x^{5}}

Differentiate the following questions w.r.t. x.

$e^{x} + e^{x^{2}} + . . . . . . . + e^{x^{5}}$

Integrate the following functions w.r.t. x.

$\int \frac{e^{x}}{(1 + e^{x}) (2 + e^{x})} d x .$

e^{x}

x

y = \frac{sin x}{e^{x}}

x

Join BYJU'S Learning Program