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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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