What is (\partial)/(\partial x)((-4x^5)/(4y^4)) ?

The answer to (\partial)/(\partial x)((-4x^5)/(4y^4)) is -(5x^4)/(y^4)

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(\partial)/(\partial x)((-4x^5)/(4y^4))

\frac{\partial}{\partial x} (\frac{- 4 x ^{5}}{4 y ^{4}})

- \frac{5 x ^{4}}{y ^{4}}

Solution steps

\frac{\partial}{\partial x} (\frac{- 4 x ^{5}}{4 y ^{4}})

Simplify

\frac{- 4 x ^{5}}{4 y ^{4}} : - \frac{x ^{5}}{y ^{4}}

= \frac{\partial}{\partial x} (- \frac{x ^{5}}{y ^{4}})

Treat

y

as a constant

Take the constant out:

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

= - \frac{1}{y ^{4}} \frac{\partial}{\partial x} (x^{5})

Apply the Power Rule:

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

= - \frac{1}{y ^{4}} \cdot 5 x^{5 - 1}

Simplify

- \frac{1}{y ^{4}} \cdot 5 x^{5 - 1} : - \frac{5 x ^{4}}{y ^{4}}

= - \frac{5 x ^{4}}{y ^{4}}

\frac{d y}{d x} y = x

- x^{2} + 3 x + 7

\frac{d}{d y} (\frac{y}{z})

\int \frac{1}{x ^{2} + 4 x + 68} d x

\frac{\partial}{\partial x} (arctan (\frac{x}{y}))

What is (\partial)/(\partial x)((-4x^5)/(4y^4)) ?
The answer to (\partial)/(\partial x)((-4x^5)/(4y^4)) is -(5x^4)/(y^4)