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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int (x^{2} + 1)^{\frac{3}{2}} d x

\int - 15 x^{4} (- 3 x^{5} - 1)^{5} d x

\frac{d}{d x} (x ln (4 x))

4 - x, 0, - 2, 6

y = 1, x = y^{\frac{5}{2}}, [0, 1]

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