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Popular >

derivative of (e^{8x})/x

Solution

derivative of

\frac{e ^{8 x}}{x}

Solution

\frac{8 e ^{8 x} x - e ^{8 x}}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{8 x}}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{8 x} ) x - \frac{d x}{d x} e ^{8 x}}{x ^{2}}

\frac{d}{d x} (e^{8 x}) = e^{8 x} \cdot 8

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

= \frac{e ^{8 x} \cdot 8 x - 1 \cdot e ^{8 x}}{x ^{2}}

Simplify

= \frac{8 e ^{8 x} x - e ^{8 x}}{x ^{2}}

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n = 1 \sum \infty 3 (\frac{1}{3})^{n - 1}

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\frac{d ^{3}}{d x ^{3}} (x^{4})

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derivative of ((4x^2-1/2 x)/((9x+8)))

\frac{d}{d x} (\frac{( 4 x ^{2} - \frac{1}{2} x )}{( 9 x + 8 )})

derivative of sqrt(1.8x+2.5)

\frac{d}{d x} (1.8 x + 2.5)

Frequently Asked Questions (FAQ)

What is the derivative of (e^{8x})/x ?
The derivative of (e^{8x})/x is (8e^{8x}x-e^{8x})/(x^2)
What is the first derivative of (e^{8x})/x ?
The first derivative of (e^{8x})/x is (8e^{8x}x-e^{8x})/(x^2)