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Popular >

derivative of (x^2/(x-7))

Solution

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

Solution

\frac{x ^{2} - 14 x}{( x - 7 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( x - 7 ) - \frac{d}{d x} ( x - 7 ) x ^{2}}{( x - 7 ) ^{2}}

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

\frac{d}{d x} (x - 7) = 1

= \frac{2 x ( x - 7 ) - 1 \cdot x ^{2}}{( x - 7 ) ^{2}}

Simplify

\frac{2 x ( x - 7 ) - 1 \cdot x ^{2}}{( x - 7 ) ^{2}} : \frac{x ^{2} - 14 x}{( x - 7 ) ^{2}}

= \frac{x ^{2} - 14 x}{( x - 7 ) ^{2}}

Popular Examples

integral from 0 to 1 of 2pi(x+11)(x^2)

\int_{0}^{1} 2 π (x + 11) (x^{2}) d x

integral of (arctan(x))/(x^2)

\int \frac{arctan ( x )}{x ^{2}} d x

derivative of (x+1/((x-1)^2))

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

integral of x/(x^2+36)

\int \frac{x}{x ^{2} + 36} d x

(\partial)/(\partial x)((3+x^2-3y^2)^{1/2})

\frac{\partial}{\partial x} ((3 + x^{2} - 3 y^{2})^{\frac{1}{2}})

Frequently Asked Questions (FAQ)

What is the derivative of (x^2/(x-7)) ?
The derivative of (x^2/(x-7)) is (x^2-14x)/((x-7)^2)
What is the first derivative of (x^2/(x-7)) ?
The first derivative of (x^2/(x-7)) is (x^2-14x)/((x-7)^2)