Expert Answer to "Find the derivatives of the functions. f(x)=xex" - Plainmath

Lipossig

Answered question

2021-05-29

Find the derivatives of the functions.

f (x) = x e^{x}

Answer & Explanation

Ezra Herbert

Skilled2021-05-30Added 99 answers

f (x) = x e^{x}

Diffetrentiate both sides with respect to x

f^{'} (x) = \frac{d}{d x} [x e^{x}]

Apply the product rule

f^{'} (x) = x \frac{d}{d x} [e^{x}] + e^{x} \frac{d}{d x} [x]

Where

\frac{d}{d x} [e^{x}] = e^{x}

and

\frac{d}{d x} [x] = 1

f^{'} (x) = x (e^{x} + e^{x} (1)

f^{'} (x) = x e^{x} + e^{x}

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