Get the solution to "Find the derivatives of the functions y=x2e−2x"

Harlen Pritchard

Answered question

2021-10-09

Find the derivatives of the functions

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

Answer & Explanation

Talisha

Skilled2021-10-10Added 93 answers

Step 1
Given:
$y = x^{2} e^{- \frac{2}{x}}$
Formula Used:
$(f * g)^{'} = f^{'} * g + f * g^{'}$
Step 2
Calculation:
$y = x^{2} e^{- \frac{2}{x}}$
The derivative of the the function is given by
$y = x^{2} e^{- \frac{2}{x}}$
$\frac{d y}{d x} = \frac{d}{d x} (x^{2} e^{- \frac{2}{x}})$
$\frac{d y}{d x} = \frac{d (x^{2})}{d x} \times e^{- \frac{2}{x}} + x^{2} \times \frac{d (e^{- \frac{2}{x}})}{d x}$
$\frac{d y}{d x} = 2 x e^{- \frac{2}{x}} + x^{2} e^{- \frac{2}{x}} \times \frac{d}{d x} (\frac{- 2}{x})$
$\frac{d y}{d x} = 2 x e^{- \frac{2}{x}} + x^{2} e^{- \frac{2}{x}} \times \frac{2}{x^{2}}$
$\frac{d y}{d x} = 2 x e^{- \frac{2}{x}} + 2 e^{- \frac{2}{x}}$

Jeffrey Jordon

Expert2022-11-14Added 2605 answers

Answer is given below (on video)

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