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Popular >

derivative of f(x)=(x^2)/(x+5)

Solution

derivative of

f (x) = \frac{x ^{2}}{x + 5}

Solution

\frac{x ^{2} + 10 x}{( x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{x + 5})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 x ( x + 5 ) - 1 \cdot x ^{2}}{( x + 5 ) ^{2}} : \frac{x ^{2} + 10 x}{( x + 5 ) ^{2}}

= \frac{x ^{2} + 10 x}{( x + 5 ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^2)/(x+5) ?
The derivative of f(x)=(x^2)/(x+5) is (x^2+10x)/((x+5)^2)
What is the first derivative of f(x)=(x^2)/(x+5) ?
The first derivative of f(x)=(x^2)/(x+5) is (x^2+10x)/((x+5)^2)