What is (\partial)/(\partial x)(x^{-2}*y/(x^3)) ?

The answer to (\partial)/(\partial x)(x^{-2}*y/(x^3)) is -(5y)/(x^6)

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(\partial)/(\partial x)(x^{-2}*y/(x^3))

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

- \frac{5 y}{x ^{6}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial x} (x^{- 2} \frac{1}{x ^{3}})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{- 2}, g = \frac{1}{x ^{3}}

= y (\frac{\partial}{\partial x} (x^{- 2}) \frac{1}{x ^{3}} + \frac{\partial}{\partial x} (\frac{1}{x ^{3}}) x^{- 2})

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

\frac{\partial}{\partial x} (\frac{1}{x ^{3}}) = - \frac{3}{x ^{4}}

= y ((- \frac{2}{x ^{3}}) \frac{1}{x ^{3}} + (- \frac{3}{x ^{4}}) x^{- 2})

Simplify

y ((- \frac{2}{x ^{3}}) \frac{1}{x ^{3}} + (- \frac{3}{x ^{4}}) x^{- 2}) : - \frac{5 y}{x ^{6}}

= - \frac{5 y}{x ^{6}}

What is (\partial)/(\partial x)(x^{-2}*y/(x^3)) ?
The answer to (\partial)/(\partial x)(x^{-2}*y/(x^3)) is -(5y)/(x^6)