What is (\partial)/(\partial y)((ax)/(y^2)) ?

The answer to (\partial)/(\partial y)((ax)/(y^2)) is -(2ax)/(y^3)

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(\partial)/(\partial y)((ax)/(y^2))

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

- \frac{2 a x}{y ^{3}}

Solution steps

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

Treat

a, x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= a x (- 2 y^{- 2 - 1})

Simplify

a x (- 2 y^{- 2 - 1}) : - \frac{2 a x}{y ^{3}}

= - \frac{2 a x}{y ^{3}}

\int \frac{1}{cos ( 8 x )} d x

\int_{0}^{2} 6 x (2 - x) d x

(2 x - 3) e^{2 - x}

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

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

What is (\partial)/(\partial y)((ax)/(y^2)) ?
The answer to (\partial)/(\partial y)((ax)/(y^2)) is -(2ax)/(y^3)