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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (ln (\frac{1 + x}{1 - x}))

\frac{d}{d x} (sin (3 x y))

\int x^{2} 5^{x^{3}} d x

y = 4 sec (5 x)

\int_{0}^{3} \frac{1}{1 - x} d x

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