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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}}

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sum from n=1 to infinity of sin(1/n)

n = 1 \sum \infty sin (\frac{1}{n})

(\partial)/(\partial x)(y^2sin(xz))

\frac{\partial}{\partial x} (y^{2} sin (x z))

limit as x approaches 4+of 1/(x^3-64)

x \to 4 + lim (\frac{1}{x ^{3} - 64})

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\int sec^{6} (2 x) d x

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\int \frac{4}{5 + 2 x - x ^{2}} d x

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)