"Find derivatives of the functions defined as follows:..." solved and explained

College
Calculus and Analysis
Differential Calculus
Derivatives

Kaycee Roche

Answered question

2021-10-05

Find derivatives of the functions defined as follows:

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

Answer & Explanation

Clelioo

Skilled2021-10-06Added 88 answers

Step 1
From the given data:
Step 2
$\frac{d}{d x} (x^{2} e^{- 2 x})$
Applying the product rule:
$(f * g)^{'} = f^{'} * g + f * g^{'}$
$f = x^{2}, g = e^{- 2 x}$
$= \frac{d}{d x} (x^{2}) (e^{- 2 x}) + \frac{d}{d x} (e^{- 2 x}) x^{2}$
$= 2 x \cdot e^{- 2 x} + (- 2 e^{- 2 x} x^{2})$
$= 2 x e^{- 2 x} - 2 e^{- 2 x} x^{2}$
$= 2 x e^{- 2 x} - 2 x^{2} e^{- 2 x}$
$= 2 x e^{- 2 x} (1 - x)$

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