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Popular >

derivative of f(x)= x/(x-6)

Solution

derivative of

f (x) = \frac{x}{x - 6}

Solution

- \frac{6}{( x - 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x - 6})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x - 6 ) - \frac{d}{d x} ( x - 6 ) x}{( x - 6 ) ^{2}}

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

\frac{d}{d x} (x - 6) = 1

= \frac{1 \cdot ( x - 6 ) - 1 \cdot x}{( x - 6 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 6 ) - 1 \cdot x}{( x - 6 ) ^{2}} : - \frac{6}{( x - 6 ) ^{2}}

= - \frac{6}{( x - 6 ) ^{2}}

Popular Examples

tangent of f(x)=5x^2+7x tangent of

f (x) = 5 x^{2} + 7 x

derivative of 1/(2x-8/(3x^2))

\frac{d}{d x} (\frac{1}{2 x} - \frac{8}{3 x ^{2}})

integral of (x^3-2x^2)^3

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

limit as x approaches 0-of e^{7/x}

x \to 0 - lim (e^{\frac{7}{x}})

integral of 1/((x+a)^2)

\int \frac{1}{( x + a ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)= x/(x-6) ?
The derivative of f(x)= x/(x-6) is -6/((x-6)^2)
What is the first derivative of f(x)= x/(x-6) ?
The first derivative of f(x)= x/(x-6) is -6/((x-6)^2)