What is (\partial)/(\partial x)((7y)/(x^{1/2)}) ?

The answer to (\partial)/(\partial x)((7y)/(x^{1/2)}) is -(7y)/(2x^{3/2)}

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(\partial)/(\partial x)((7y)/(x^{1/2)})

\frac{\partial}{\partial x} (\frac{7 y}{x ^{\frac{1}{2}}})

- \frac{7 y}{2 x ^{\frac{3}{2}}}

Solution steps

\frac{\partial}{\partial x} (\frac{7 y}{x ^{\frac{1}{2}}})

Treat

y

as a constant

Take the constant out:

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

= 7 y \frac{\partial}{\partial x} (\frac{1}{x ^{\frac{1}{2}}})

Apply exponent rule:

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

= 7 y \frac{\partial}{\partial x} (x^{- \frac{1}{2}})

Apply the Power Rule:

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

= 7 y (- \frac{1}{2} x^{- \frac{1}{2} - 1})

Simplify

7 y (- \frac{1}{2} x^{- \frac{1}{2} - 1}) : - \frac{7 y}{2 x ^{\frac{3}{2}}}

= - \frac{7 y}{2 x ^{\frac{3}{2}}}

What is (\partial)/(\partial x)((7y)/(x^{1/2)}) ?
The answer to (\partial)/(\partial x)((7y)/(x^{1/2)}) is -(7y)/(2x^{3/2)}