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Clifland

Answered question

2021-10-12

Derivatives Find and simplify the derivative of the following functions

h (x) = \frac{x + 1}{x^{2} e^{x}}

Answer & Explanation

Laaibah Pitt

Skilled2021-10-13Added 98 answers

Given:
The given function is

h (x) = \frac{x + 1}{x^{2} e^{x}}

Calculation:

h^{'} (x) = \frac{d}{d x} (\frac{x + 1}{x^{2} e^{x}})

= \frac{(x^{2} e^{x}) \frac{d}{d x} (x + 1) - (x + 1) \frac{d}{d x} (x^{2} e^{x})}{{(x^{2} e^{x})}^{2}}

= \frac{(x^{2} e^{x}) (1) - (x + 1) (x^{2} e^{x} + 2 x e^{x})}{x^{4} e^{2 x}}

= \frac{x^{2} e^{x} - x^{3} e^{x} - 2 x^{2} e^{x} - x^{2} e^{x} - 2 x e^{x}}{x e^{x} (x^{3} e^{x})}

= \frac{- (x^{2} + 2 x + 2) x e^{x}}{x e^{x} (x^{3} e^{x})}

= \frac{- (x^{2} + 2 x + 2)}{x^{3} e^{x}}

Jeffrey Jordon

Expert2022-08-14Added 2605 answers

Answer is given below (on video)

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