What is the derivative of (x^2/(x+5)) ?

The derivative of (x^2/(x+5)) is (x^2+10x)/((x+5)^2)

What is the first derivative of (x^2/(x+5)) ?

The first derivative of (x^2/(x+5)) is (x^2+10x)/((x+5)^2)

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

\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}}

f (x) = 5 x^{4}

x \to 0 lim (\frac{2 + x}{2 - x})

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

\int \frac{tan ^{3} ( ln ( x ) )}{9 x} d x

\frac{d}{d x} (5 - 6 x)

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