Question

pls help me fastttttttt​

Answer 1

ANSWER.

• xeˣ(x + 2)

SOLUTION.

Given –

$\tt \implies y = {x}^{2}. {e}^{x}$

$\tt \implies \dfrac{dy}{dx} = \dfrac{d}{dx}({x}^{2}. {e}^{x})$

Using differentiation rule,

$\tt \implies \dfrac{d}{dx}(f \times g) = g \dfrac{d}{dx}(f) + f \dfrac{d}{dx}(g)$

$\tt \implies \dfrac{dy}{dx} = {e}^{x} \dfrac{d}{dx}({x}^{2}) + {x}^{2} \times \dfrac{d}{dx}( {e}^{x} )$

Note:

$\tt \implies \dfrac{d}{dx}( {x}^{n} ) = n {x}^{n - 1}$

$\tt \implies \dfrac{d}{dx}( {e}^{x} ) = {e}^{x}$

Therefore,

$\tt \implies \dfrac{dy}{dx} = {e}^{x}.2 {x}^{2 - 1} + {x}^{2} {e}^{x}$

$\tt \implies \dfrac{dy}{dx} = 2x{e}^{x} + {x}^{2} {e}^{x}$

$\tt \implies \dfrac{dy}{dx} = x{e}^{x}(2+x)$

$\tt \implies \dfrac{dy}{dx} = x{e}^{x}(x + 2)$

So, option A is the right answer.