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Popular >

derivative of f(x)= x/(x-3)

Solution

derivative of

f (x) = \frac{x}{x - 3}

Solution

- \frac{3}{( x - 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x - 3})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x - 3) = 1

= \frac{1 \cdot ( x - 3 ) - 1 \cdot x}{( x - 3 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 3 ) - 1 \cdot x}{( x - 3 ) ^{2}} : - \frac{3}{( x - 3 ) ^{2}}

= - \frac{3}{( x - 3 ) ^{2}}

Popular Examples

derivative of f(x)=(x^2+x-2)/(x^3+6)derivative of

f (x) = \frac{x ^{2} + x - 2}{x ^{3} + 6}

derivative of 2xsqrt(4-x^2)

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

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\frac{d}{d x} (ln (e^{x} - e^{a}))

derivative of e^{x^2+9x}

\frac{d}{d x} (e^{x^{2} + 9 x})

integral of sec^3(x)tan^5(x)

\int sec^{3} (x) tan^{5} (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)= x/(x-3) ?
The derivative of f(x)= x/(x-3) is -3/((x-3)^2)
What is the first derivative of f(x)= x/(x-3) ?
The first derivative of f(x)= x/(x-3) is -3/((x-3)^2)