What is the derivative of (e^{10x}+e^{-10x})/x ?

The derivative of (e^{10x}+e^{-10x})/x is (10e^{10x}x-10e^{-10x}x-e^{10x}-e^{-10x})/(x^2)

What is the first derivative of (e^{10x}+e^{-10x})/x ?

The first derivative of (e^{10x}+e^{-10x})/x is (10e^{10x}x-10e^{-10x}x-e^{10x}-e^{-10x})/(x^2)

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derivative of

\frac{e ^{10 x} + e ^{- 10 x}}{x}

\frac{10 e ^{10 x} x - 10 e ^{- 10 x} x - e ^{10 x} - e ^{- 10 x}}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{10 x} + e ^{- 10 x}}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{10 x} + e ^{- 10 x} ) x - \frac{d x}{d x} ( e ^{10 x} + e ^{- 10 x} )}{x ^{2}}

\frac{d}{d x} (e^{10 x} + e^{- 10 x}) = e^{10 x} \cdot 10 - 10 e^{- 10 x}

\frac{d x}{d x} = 1

= \frac{( e ^{10 x} \cdot 10 - 10 e ^{- 10 x} ) x - 1 \cdot ( e ^{10 x} + e ^{- 10 x} )}{x ^{2}}

Simplify

\frac{( e ^{10 x} \cdot 10 - 10 e ^{- 10 x} ) x - 1 \cdot ( e ^{10 x} + e ^{- 10 x} )}{x ^{2}} : \frac{10 e ^{10 x} x - 10 e ^{- 10 x} x - e ^{10 x} - e ^{- 10 x}}{x ^{2}}

= \frac{10 e ^{10 x} x - 10 e ^{- 10 x} x - e ^{10 x} - e ^{- 10 x}}{x ^{2}}

\frac{d}{d x} (2 (ln (x)))

\int_{0}^{1.5} (\frac{3}{2} - x)^{2} d x

y^{^{''}} - 8 y^{^{'}} + 16 y = t^{- 8} e^{4 t}

\int (cos^{4} (x) sin (x)) d x

\int (x^{2} + 1) (x^{3} + 3 x)^{4} d x

What is the derivative of (e^{10x}+e^{-10x})/x ?
The derivative of (e^{10x}+e^{-10x})/x is (10e^{10x}x-10e^{-10x}x-e^{10x}-e^{-10x})/(x^2)
What is the first derivative of (e^{10x}+e^{-10x})/x ?
The first derivative of (e^{10x}+e^{-10x})/x is (10e^{10x}x-10e^{-10x}x-e^{10x}-e^{-10x})/(x^2)