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

The answer to (\partial)/(\partial x)(-4x^5y^{-5}) is -(20x^4)/(y^5)

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

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

- \frac{20 x ^{4}}{y ^{5}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

- 4 y^{- 5} \cdot 5 x^{5 - 1} : - \frac{20 x ^{4}}{y ^{5}}

= - \frac{20 x ^{4}}{y ^{5}}

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

\frac{d}{d x} (ln (x^{11}))

\frac{\partial}{\partial x} (x^{2} y^{3} (6 - x - y))

\frac{d}{d x} (x^{15})

y^{^{'}} = sin (x) y + e^{x}

What is (\partial)/(\partial x)(-4x^5y^{-5}) ?
The answer to (\partial)/(\partial x)(-4x^5y^{-5}) is -(20x^4)/(y^5)