What is the derivative of (x^2/(sqrt(x^2+9))) ?

The derivative of (x^2/(sqrt(x^2+9))) is (x^3+18x)/((x^2+9)sqrt(x^2+9))

What is the first derivative of (x^2/(sqrt(x^2+9))) ?

The first derivative of (x^2/(sqrt(x^2+9))) is (x^3+18x)/((x^2+9)sqrt(x^2+9))

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\frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 9})

\frac{x ^{3} + 18 x}{( x ^{2} + 9 ) x ^{2} + 9}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 9})

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} + 9 - \frac{d}{d x} ( x ^{2} + 9 ) x ^{2}}{( x ^{2} + 9 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 9) = \frac{x}{x ^{2} + 9}

= \frac{2 x x ^{2} + 9 - \frac{x}{x ^{2} + 9} x ^{2}}{( x ^{2} + 9 ) ^{2}}

Simplify

\frac{2 x x ^{2} + 9 - \frac{x}{x ^{2} + 9} x ^{2}}{( x ^{2} + 9 ) ^{2}} : \frac{x ^{3} + 18 x}{( x ^{2} + 9 ) x ^{2} + 9}

= \frac{x ^{3} + 18 x}{( x ^{2} + 9 ) x ^{2} + 9}

\int (x^{2} - 2 x) d x

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\frac{d}{d x} (7 (e^{x} cos (x) - e^{x} sin (x)))

What is the derivative of (x^2/(sqrt(x^2+9))) ?
The derivative of (x^2/(sqrt(x^2+9))) is (x^3+18x)/((x^2+9)sqrt(x^2+9))
What is the first derivative of (x^2/(sqrt(x^2+9))) ?
The first derivative of (x^2/(sqrt(x^2+9))) is (x^3+18x)/((x^2+9)sqrt(x^2+9))