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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

x^{2} - 1, \frac{1}{2} x^{2}

\int \frac{sin ( 2 x )}{2 + 2 sin ^{2} ( x )} d x

y^{^{''}} + 49 y = - 49 sec^{2} (7 x)

(9 x^{2} + y - 1) - (4 y - x) y^{^{'}} = 0

ln (\frac{1}{1 - x})

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