What is (\partial)/(\partial x)((y^2)/(4-x^2)) ?

The answer to (\partial)/(\partial x)((y^2)/(4-x^2)) is (2y^2x)/((4-x^2)^2)

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(\partial)/(\partial x)((y^2)/(4-x^2))

\frac{\partial}{\partial x} (\frac{y ^{2}}{4 - x ^{2}})

\frac{2 y ^{2} x}{( 4 - x ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{y ^{2}}{4 - x ^{2}})

Treat

y

as a constant

Take the constant out:

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

= y^{2} \frac{\partial}{\partial x} (\frac{1}{4 - x ^{2}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= y^{2} \frac{\partial}{\partial x} ((4 - x^{2})^{- 1})

Apply the chain rule:

- \frac{1}{( 4 - x ^{2} ) ^{2}} \frac{\partial}{\partial x} (4 - x^{2})

= - \frac{1}{( 4 - x ^{2} ) ^{2}} \frac{\partial}{\partial x} (4 - x^{2})

\frac{\partial}{\partial x} (4 - x^{2}) = - 2 x

= y^{2} (- \frac{1}{( 4 - x ^{2} ) ^{2}} (- 2 x))

Simplify

y^{2} (- \frac{1}{( 4 - x ^{2} ) ^{2}} (- 2 x)) : \frac{2 y ^{2} x}{( 4 - x ^{2} ) ^{2}}

= \frac{2 y ^{2} x}{( 4 - x ^{2} ) ^{2}}

\int \frac{1}{- x ^{2} + 6 x - 10} d x

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

\int \frac{( ln ( x ) ) ^{2}}{2} d x

y^{^{'}} = 6 y^{2} + x y^{2}, y (0) = 1

\frac{d ^{2}}{d x ^{2}} (\frac{2000 t}{4 t + 75})

What is (\partial)/(\partial x)((y^2)/(4-x^2)) ?
The answer to (\partial)/(\partial x)((y^2)/(4-x^2)) is (2y^2x)/((4-x^2)^2)