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

The answer to (\partial)/(\partial x)((5y)/(x^5)) is -(25y)/(x^6)

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

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

- \frac{25 y}{x ^{6}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

= 5 y (- 5 x^{- 5 - 1})

Simplify

5 y (- 5 x^{- 5 - 1}) : - \frac{25 y}{x ^{6}}

= - \frac{25 y}{x ^{6}}

x y^{^{'}} - 3 y^{2} = 0

3 e^{- 7 t} cos (\frac{t}{3} + \frac{π}{3})

\frac{d y}{d x - y ^{2}} = 36

x \to 0 lim (\frac{cos ( 4 x ) - 1}{x})

\frac{\partial}{\partial y} (2 x sin (y))

What is (\partial)/(\partial x)((5y)/(x^5)) ?
The answer to (\partial)/(\partial x)((5y)/(x^5)) is -(25y)/(x^6)