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

The derivative of (9x^2/(x^2+2)) is (36x)/((x^2+2)^2)

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

The first derivative of (9x^2/(x^2+2)) is (36x)/((x^2+2)^2)

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

\frac{36 x}{( x ^{2} + 2 ) ^{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

9 \cdot \frac{2 x ( x ^{2} + 2 ) - 2 x x ^{2}}{( x ^{2} + 2 ) ^{2}} : \frac{36 x}{( x ^{2} + 2 ) ^{2}}

= \frac{36 x}{( x ^{2} + 2 ) ^{2}}

\int cos (x) cos (n x) d x

\frac{\partial}{\partial x} ((1 + \frac{2}{y}) sin (x))

\int \frac{e ^{x}}{( 4 + 9 e ^{2 x} )} d x

\frac{1}{s} \cdot \frac{1}{s ^{2} + \frac{s}{2} + \frac{1}{2}}

\int \frac{1}{x ^{2} + 8 x + 52} d x

What is the derivative of (9x^2/(x^2+2)) ?
The derivative of (9x^2/(x^2+2)) is (36x)/((x^2+2)^2)
What is the first derivative of (9x^2/(x^2+2)) ?
The first derivative of (9x^2/(x^2+2)) is (36x)/((x^2+2)^2)