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

The derivative of (e^{2x}-e^x+e^{-3x}/(e^x)) is -(-e^{5x}+4)/(e^{4x)}

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

The first derivative of (e^{2x}-e^x+e^{-3x}/(e^x)) is -(-e^{5x}+4)/(e^{4x)}

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

- \frac{- e ^{5 x} + 4}{e ^{4 x}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( e ^{2 x} \cdot 2 - e ^{x} - 3 e ^{- 3 x} ) e ^{x} - e ^{x} ( e ^{2 x} - e ^{x} + e ^{- 3 x} )}{( e ^{x} ) ^{2}} : - \frac{- e ^{5 x} + 4}{e ^{4 x}}

= - \frac{- e ^{5 x} + 4}{e ^{4 x}}

\frac{\partial}{\partial x} (2 x)

\int \frac{1}{x ^{2} + 1} d x

\frac{\partial}{\partial x} (z sin (x))

\frac{d}{d x} (ln (4 x^{2}))

sin^{2} (x), sin^{4} (x), 0, π

What is the derivative of (e^{2x}-e^x+e^{-3x}/(e^x)) ?
The derivative of (e^{2x}-e^x+e^{-3x}/(e^x)) is -(-e^{5x}+4)/(e^{4x)}
What is the first derivative of (e^{2x}-e^x+e^{-3x}/(e^x)) ?
The first derivative of (e^{2x}-e^x+e^{-3x}/(e^x)) is -(-e^{5x}+4)/(e^{4x)}