What is (\partial)/(\partial x)((7y)/(x^5)) ?

The answer to (\partial)/(\partial x)((7y)/(x^5)) is -(35y)/(x^6)

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(\partial)/(\partial x)((7y)/(x^5))

\frac{\partial}{\partial x} (\frac{7 y}{x ^{5}})

- \frac{35 y}{x ^{6}}

Solution steps

\frac{\partial}{\partial x} (\frac{7 y}{x ^{5}})

Treat

y

as a constant

Take the constant out:

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

= 7 y \frac{\partial}{\partial x} (\frac{1}{x ^{5}})

Apply exponent rule:

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

= 7 y \frac{\partial}{\partial x} (x^{- 5})

Apply the Power Rule:

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

= 7 y (- 5 x^{- 5 - 1})

Simplify

7 y (- 5 x^{- 5 - 1}) : - \frac{35 y}{x ^{6}}

= - \frac{35 y}{x ^{6}}

\frac{\partial}{\partial y} (ln (x^{6} + y^{4}))

\int_{0}^{2} x^{4} - 2 x^{3} d x

\frac{\partial}{\partial x} (sin^{2} (m x + n y))

f (x) = \frac{2}{x}, at x = - 5

What is (\partial)/(\partial x)((7y)/(x^5)) ?
The answer to (\partial)/(\partial x)((7y)/(x^5)) is -(35y)/(x^6)