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Popular >

derivative of x/(x-4)

Solution

derivative of

\frac{x}{x - 4}

Solution

- \frac{4}{( x - 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x - 4})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x - 4 ) - \frac{d}{d x} ( x - 4 ) x}{( x - 4 ) ^{2}}

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

\frac{d}{d x} (x - 4) = 1

= \frac{1 \cdot ( x - 4 ) - 1 \cdot x}{( x - 4 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 4 ) - 1 \cdot x}{( x - 4 ) ^{2}} : - \frac{4}{( x - 4 ) ^{2}}

= - \frac{4}{( x - 4 ) ^{2}}

Popular Examples

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\frac{- 2 x ^{2} + 9}{9 - x ^{2}}

integral from 7 to 8 of (1/(x^2)-1)

\int_{7}^{8} (\frac{1}{x ^{2}} - 1) d x

((ln(x))/(x^2))^'

(\frac{ln ( x )}{x ^{2}})^{^{'}}

(\partial)/(\partial x)(cos^7(x^9y^5))

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derivative of y=(4-xe^x)/(x+e^x)derivative of

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Frequently Asked Questions (FAQ)

What is the derivative of x/(x-4) ?
The derivative of x/(x-4) is -4/((x-4)^2)
What is the first derivative of x/(x-4) ?
The first derivative of x/(x-4) is -4/((x-4)^2)