Question: "Find derivatives of the functions defined as follows:..."

generals336

Answered question

2021-06-06

Find derivatives of the functions defined as follows:

y = x^{e x}

liingliing8

Skilled2021-06-07Added 95 answers

Step 1
Find derivatives of the functions defined as follows:

y = x^{e x}

Step 2
We have

y = x e^{x}

.....(1)
Differentiating equation(1), w.r.t x, we get

\Rightarrow \frac{d y}{d x} = \frac{d}{d x} (x e^{x})

\Rightarrow \frac{d y}{d x} = x . \frac{d}{d x} (e^{x}) + e^{x} . \frac{d}{d x} (x)

, Applying the product rule

\Rightarrow \frac{d y}{d x} = x . e^{x} + e^{x} .1

\Rightarrow \frac{d y}{d x} = x e^{x} + e^{x}

\Rightarrow \frac{d y}{d x} = e^{x} (x + 1)

Hence,

\frac{d y}{d x} = e^{x} (x + 1)

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