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

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

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

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

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

\frac{e ^{2 x} - 1}{e ^{x}}

Solution steps

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

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

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

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

Simplify

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

= \frac{e ^{2 x} - 1}{e ^{x}}

\int_{0}^{1} 11 x x^{2} + 36 d x

x y^{^{'}} + 2 y^{^{'}} - (x + 2) sin (x) + y = 0

\frac{\partial}{\partial x} ((x^{2} y - y^{3})^{5})

- \frac{e ^{(- 2 s)}}{( s ^{2} - 4 s + 4 )}

\int x^{5} e^{4 x} d x

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