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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Quotient Rule:

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

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

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

\frac{\partial}{\partial x} (y^{2} - x) = - 1

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

Simplify

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

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

\frac{d}{d x} (\frac{1 + csc ( x ^{7} )}{1 - cot ( x ^{7} )})

\frac{9}{x - 6}

\int_{1}^{5} 1 + (4)^{2} d x

\frac{d}{d x} (\frac{3}{2 x})

x \to 1 lim (- 3 a x + b)

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