Resolved: "Find derivatives of the function defined as follows...." - Plainmath

Bevan Mcdonald

Answered question

2021-10-15

Find derivatives of the function defined as follows.

y = \frac{x^{2}}{e^{x}}

Answer & Explanation

dessinemoie

Skilled2021-10-16Added 90 answers

Step 1
The given function is

y = \frac{x^{2}}{e^{x}}

.
The derivative can be obtained using the formula

{(\frac{u}{v})}^{'} = \frac{v u^{'} - u v^{'}}{v^{2}}

.
Step 2
The derivative is obtained as follows.

\frac{d y}{d x} = \frac{d}{d x} (\frac{x^{2}}{e^{x}})

= \frac{e^{x} \frac{d}{d x} (x^{2}) - x^{2} \frac{d}{d x} (e^{x})}{{(e^{x})}^{2}}

= \frac{e^{x} (2 x) - x^{2} (e^{x})}{e^{2 x}}

= \frac{2 x e^{x} - x^{2} e^{x}}{e^{x} \cdot e^{x}}

= \frac{2 x - x^{2}}{e^{x}}

= \frac{x (2 - x)}{e^{x}}

Jeffrey Jordon

Expert2022-08-14Added 2605 answers

Answer is given below (on video)

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