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

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

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

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

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Popular >

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

\frac{3 e ^{3 x} x - 3 e ^{- 3 x} x - e ^{3 x} - e ^{- 3 x}}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d y}{d t} = (- csc (t) cot (t)) e^{- c s c (t)}

x \to \infty lim (- 3 x^{3})

x \to 0 - lim (1 - x^{2})

x \to 0 lim ((1 - 4 x)^{\frac{7}{x}})

n = 1 \sum \infty \frac{35}{- 6 ^{n}}

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