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Let
f(x)=x^(2)e^(x).

f^(')(x)=

Let $f(x)=x^{2} e^{x}$ . $\newline$ $f^{\prime}(x)=$

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Write a formula for an arithmetic sequence

Full solution

Q. Let

f(x)=x^{2} e^{x}

.

\newline

f^{\prime}(x)=

Identify rule: Identify the rule to use for differentiation; here, we need the product rule since $f(x)$ is the product of two functions, $x^2$ and $e^x$ .
Apply product rule: Apply the product rule: $(u*v)' = u'v + uv'$ , where $u = x^2$ and $v = e^x$ .
Differentiate $u$ : Differentiate $u = x^2$ to get $u' = 2x$ .
Differentiate $v$ : Differentiate $v = e^x$ to get $v' = e^x$ .
Plug into formula: Plug $u'$ , $u$ , $v'$ , and $v$ into the product rule formula: $f'(x) = 2x \cdot e^x + x^2 \cdot e^x$ .
Simplify expression: Combine like terms to simplify the expression: $f'(x) = (2x + x^2) \cdot e^x$ .
Correct mistake: Realize there's a mistake in the previous step; we don't actually combine terms like that. Correct the expression: $f'(x) = 2x \cdot e^x + x^2 \cdot e^x$ .

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