What is (\partial}{\partial x}(\frac{y^3)/x) ?

The answer to (\partial}{\partial x}(\frac{y^3)/x) is -(y^3)/(x^2)

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

= y^{3} (- 1 \cdot x^{- 1 - 1})

Simplify

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

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

\frac{d}{d x} (3 x^{2} + 4 x + 1)

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

\int ((2 - x)^{\frac{1}{2}}) d x

f (x) = x^{4} ln (x)

y = 7 x - x^{2} (1.6)

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