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

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

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Solution

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

Differentiate both sides w.r.t. x, we get

$\frac{d}{d x} y = \frac{d}{d x} {e^{x} + e^{x^{2}} + e^{x^{3}} + e^{x^{4}} + e^{x^{5}}} = \frac{d}{d x} (e^{x}) + \frac{d}{d x} (e^{x^{2}}) + \frac{d}{d x} (e^{x^{3}}) + \frac{d v}{d x} (e^{x^{4}}) + \frac{d}{d x} (e^{x^{5}}) = e^{x} + e^{x^{2}} \frac{d}{d x} (x^{2}) + e^{x^{3}} \frac{d}{d x} (x^{3}) + e^{x^{4}} \frac{d}{d x} + e^{x^{5}} \frac{d}{d x} (x^{5}) (U s i n g c h a i n r u l e) = e^{x} + e^{x^{2}} (2 x) + e^{x^{3}} (3 x^{2}) + e^{x^{4}} (4 x^{3}) + e^{x^{5}} (5 x^{4}) = e^{x} + 2 x e^{x^{2}} + 3 x^{2} e^{x^{3}} + 4 x^{3} e^{x^{4}} + 5 x^{4} e^{x^{5}}$

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Similar questions

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

x

x

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

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