What is (\partial)/(\partial y)((y^3)/(x^2)) ?

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

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(\partial)/(\partial y)((y^3)/(x^2))

\frac{\partial}{\partial y} (\frac{y ^{3}}{x ^{2}})

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

Solution steps

\frac{\partial}{\partial y} (\frac{y ^{3}}{x ^{2}})

Treat

x

as a constant

Take the constant out:

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

= \frac{1}{x ^{2}} \frac{\partial}{\partial y} (y^{3})

Apply the Power Rule:

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

= \frac{1}{x ^{2}} \cdot 3 y^{3 - 1}

Simplify

\frac{1}{x ^{2}} \cdot 3 y^{3 - 1} : \frac{3 y ^{2}}{x ^{2}}

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

y^{^{'}} = - k y^{3}

\int (\frac{1}{x} + cot (x) - sec (x)) d x

e^{3 \cdot x} \cdot (2 \cdot sin (4 \cdot x))

\int \frac{1}{( 2 y + 5 ) ^{2}} d y

n = 1 \sum \infty (\frac{2}{3})^{n}

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