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

The derivative of (x^2)/(sqrt(x^2+5)) is (x^3+10x)/((x^2+5)sqrt(x^2+5))

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

The first derivative of (x^2)/(sqrt(x^2+5)) is (x^3+10x)/((x^2+5)sqrt(x^2+5))

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derivative of

\frac{x ^{2}}{x ^{2} + 5}

\frac{x ^{3} + 10 x}{( x ^{2} + 5 ) x ^{2} + 5}

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

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

Simplify

\frac{2 x x ^{2} + 5 - \frac{x}{x ^{2} + 5} x ^{2}}{( x ^{2} + 5 ) ^{2}} : \frac{x ^{3} + 10 x}{( x ^{2} + 5 ) x ^{2} + 5}

= \frac{x ^{3} + 10 x}{( x ^{2} + 5 ) x ^{2} + 5}

What is the derivative of (x^2)/(sqrt(x^2+5)) ?
The derivative of (x^2)/(sqrt(x^2+5)) is (x^3+10x)/((x^2+5)sqrt(x^2+5))
What is the first derivative of (x^2)/(sqrt(x^2+5)) ?
The first derivative of (x^2)/(sqrt(x^2+5)) is (x^3+10x)/((x^2+5)sqrt(x^2+5))