What is (\partial)/(\partial x)(y/(2sqrt(x))-1) ?

The answer to (\partial)/(\partial x)(y/(2sqrt(x))-1) is -y/(4x^{3/2)}

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(\partial)/(\partial x)(y/(2sqrt(x))-1)

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

- \frac{y}{4 x ^{\frac{3}{2}}}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (1) = 0

= - \frac{y}{4 x ^{\frac{3}{2}}} - 0

Simplify

= - \frac{y}{4 x ^{\frac{3}{2}}}

\frac{d x}{d t} = x^{2}

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What is (\partial)/(\partial x)(y/(2sqrt(x))-1) ?
The answer to (\partial)/(\partial x)(y/(2sqrt(x))-1) is -y/(4x^{3/2)}