What is (\partial)/(\partial x)((3y)*(2x)^{-1}) ?

The answer to (\partial)/(\partial x)((3y)*(2x)^{-1}) is -(3y)/(2x^2)

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(\partial)/(\partial x)((3y)*(2x)^{-1})

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

- \frac{3 y}{2 x ^{2}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (2 x) = 2

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

Simplify

3 y (- \frac{1}{( 2 x ) ^{2}} \cdot 2) : - \frac{3 y}{2 x ^{2}}

= - \frac{3 y}{2 x ^{2}}

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What is (\partial)/(\partial x)((3y)*(2x)^{-1}) ?
The answer to (\partial)/(\partial x)((3y)*(2x)^{-1}) is -(3y)/(2x^2)