What is (\partial)/(\partial x)((6x)/((x^2+9))) ?

The answer to (\partial)/(\partial x)((6x)/((x^2+9))) is (6(-x^2+9))/((x^2+9)^2)

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(\partial)/(\partial x)((6x)/((x^2+9)))

\frac{\partial}{\partial x} (\frac{6 x}{( x ^{2} + 9 )})

\frac{6 ( - x ^{2} + 9 )}{( x ^{2} + 9 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{6 x}{( x ^{2} + 9 )})

Take the constant out:

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

= 6 \frac{\partial}{\partial x} (\frac{x}{x ^{2} + 9})

Apply the Quotient Rule:

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

= 6 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( x ^{2} + 9 ) - \frac{\partial}{\partial x} ( x ^{2} + 9 ) x}{( x ^{2} + 9 ) ^{2}}

\frac{\partial}{\partial x} (x) = 1

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

= 6 \cdot \frac{1 \cdot ( x ^{2} + 9 ) - 2 xx}{( x ^{2} + 9 ) ^{2}}

Simplify

6 \cdot \frac{1 \cdot ( x ^{2} + 9 ) - 2 xx}{( x ^{2} + 9 ) ^{2}} : \frac{6 ( - x ^{2} + 9 )}{( x ^{2} + 9 ) ^{2}}

= \frac{6 ( - x ^{2} + 9 )}{( x ^{2} + 9 ) ^{2}}

n = 0 \sum \infty \frac{n}{2 ^{n}}

9 e^{x} + x

x \to - 4 lim (\frac{x ^{2} - 2}{4 - x})

ln (5 x^{4})

\int \frac{x ^{2}}{4} d x

What is (\partial)/(\partial x)((6x)/((x^2+9))) ?
The answer to (\partial)/(\partial x)((6x)/((x^2+9))) is (6(-x^2+9))/((x^2+9)^2)