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

The derivative of (e^x+e^{-x}/(x^3)) is (e^{-x}(x(e^{2x}-1)-3(e^{2x}+1)))/(x^4)

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

The first derivative of (e^x+e^{-x}/(x^3)) is (e^{-x}(x(e^{2x}-1)-3(e^{2x}+1)))/(x^4)

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Popular >

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

\frac{e ^{- x} ( x ( e ^{2 x} - 1 ) - 3 ( e ^{2 x} + 1 ) )}{x ^{4}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

Simplify

\frac{( e ^{x} - e ^{- x} ) x ^{3} - 3 x ^{2} ( e ^{x} + e ^{- x} )}{( x ^{3} ) ^{2}} : \frac{e ^{- x} ( x ( e ^{2 x} - 1 ) - 3 ( e ^{2 x} + 1 ) )}{x ^{4}}

= \frac{e ^{- x} ( x ( e ^{2 x} - 1 ) - 3 ( e ^{2 x} + 1 ) )}{x ^{4}}

y^{3} - (14 x + 8) + 3 x y^{2} \frac{d y}{d x} = 0

\frac{\partial}{\partial y} (sin (x y) + e^{x y})

\int_{- 7}^{7} \frac{y}{49 - y ^{2}} d y

4 arcsin (x^{3})

\int_{0}^{2} (x 9 - x^{2}) d x

What is the derivative of (e^x+e^{-x}/(x^3)) ?
The derivative of (e^x+e^{-x}/(x^3)) is (e^{-x}(x(e^{2x}-1)-3(e^{2x}+1)))/(x^4)
What is the first derivative of (e^x+e^{-x}/(x^3)) ?
The first derivative of (e^x+e^{-x}/(x^3)) is (e^{-x}(x(e^{2x}-1)-3(e^{2x}+1)))/(x^4)