What is (\partial)/(\partial y)((x^2)/(y+1)) ?

The answer to (\partial)/(\partial y)((x^2)/(y+1)) is -(x^2)/((y+1)^2)

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(\partial)/(\partial y)((x^2)/(y+1))

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (- sin (2 x))

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

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

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

\int x^{n + 1} d x

What is (\partial)/(\partial y)((x^2)/(y+1)) ?
The answer to (\partial)/(\partial y)((x^2)/(y+1)) is -(x^2)/((y+1)^2)