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Popular >

derivative of f(x)= x/(x-5)

Solution

derivative of

f (x) = \frac{x}{x - 5}

Solution

- \frac{5}{( x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x - 5})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x - 5 ) - \frac{d}{d x} ( x - 5 ) x}{( x - 5 ) ^{2}}

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

\frac{d}{d x} (x - 5) = 1

= \frac{1 \cdot ( x - 5 ) - 1 \cdot x}{( x - 5 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 5 ) - 1 \cdot x}{( x - 5 ) ^{2}} : - \frac{5}{( x - 5 ) ^{2}}

= - \frac{5}{( x - 5 ) ^{2}}

Popular Examples

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\int \frac{1}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

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f (x) = (2 x^{2} - 3)^{3}

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\int 8 x^{7} sin (x^{8}) d x

e^{(x+y)}(dx+dy)+4xdx=0

e^{(x + y)} (d x + d y) + 4 x d x = 0

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θ \to \frac{π}{2} lim (θ cos (θ))

Frequently Asked Questions (FAQ)

What is the derivative of f(x)= x/(x-5) ?
The derivative of f(x)= x/(x-5) is -5/((x-5)^2)
What is the first derivative of f(x)= x/(x-5) ?
The first derivative of f(x)= x/(x-5) is -5/((x-5)^2)