Math, asked by sunilvermamahaveerat, 11 months ago

Differentiation find
$x(x + 1) \ {e}^{x}$

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Answers

Answered by omsamarth4315

Answer:

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Answered by BrainlyPopularman

ANSWER :–

$\: \frac{dy}{dx} \: = ( {x}^{2} + 3x + 1) {e}^{x} \\$

EXPLANATION :–

▪︎ According to the question –

• Let the function –

$\\ \: y \: = x(x + 1) {e}^{x} \\$

$\\ \: y \: = ( {x}^{2} + x) {e}^{x} \\$

• Now Different with respect to 'x' –

$\\ \: \frac{dy}{dx} \: = ( {x}^{2} + x) {e}^{x} + (2x + 1) {e}^{x} \\$

$\\ \: \frac{dy}{dx} \: = ( {x}^{2} + x + 2x + 1) {e}^{x} \\$

$\\ \: \frac{dy}{dx} \: = ( {x}^{2} + 3x + 1) {e}^{x} \\$

USED FORMULA :–

$\\ \: (1) \frac{d( {x}^{n} )}{dx} \: = n {x}^{n - 1} \\$

$\\ \: (2) \: \frac{d( {e}^{x} )}{dx} \: = {e}^{x} \\$

$\\ \: (3) \: \frac{d(U.V)}{dx} \: = U \frac{d(V)}{dx} + V \frac{d(U)}{dx} \\$

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