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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

11 + tan^{2} (x)

n = 0 \sum \infty p (1 - p)^{n}

e^{- x^{2}} cos (x)

\int e^{2 x} \cdot sin (3 x) d x

\frac{d}{d x} (csc^{4} (x))

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