What is the derivative of (-e^{-x}x-e^{-x}/(x^2)) ?

The derivative of (-e^{-x}x-e^{-x}/(x^2)) is (e^{-x}(x^2+2(x+1)))/(x^3)

What is the first derivative of (-e^{-x}x-e^{-x}/(x^2)) ?

The first derivative of (-e^{-x}x-e^{-x}/(x^2)) is (e^{-x}(x^2+2(x+1)))/(x^3)

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Popular >

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

\frac{e ^{- x} ( x ^{2} + 2 ( x + 1 ) )}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

\frac{e ^{- x} x x ^{2} - 2 x ( - e ^{- x} x - e ^{- x} )}{( x ^{2} ) ^{2}} : \frac{e ^{- x} ( x ^{2} + 2 ( x + 1 ) )}{x ^{3}}

= \frac{e ^{- x} ( x ^{2} + 2 ( x + 1 ) )}{x ^{3}}

\int_{- 7}^{7} (1 + 49 - x^{2}) d x

\frac{d y}{d x} = \frac{x ^{2} + 2 y ^{2}}{x y}

f (x) = \frac{1}{( x - 5 )}, at x = - 3

\frac{2 s + 1}{s ^{2} - 2 s + 2}

\int_{2}^{3} 3 x^{2} d x

What is the derivative of (-e^{-x}x-e^{-x}/(x^2)) ?
The derivative of (-e^{-x}x-e^{-x}/(x^2)) is (e^{-x}(x^2+2(x+1)))/(x^3)
What is the first derivative of (-e^{-x}x-e^{-x}/(x^2)) ?
The first derivative of (-e^{-x}x-e^{-x}/(x^2)) is (e^{-x}(x^2+2(x+1)))/(x^3)