What is the derivative of ((x^{1/2}/(sqrt(y)))^{-3/2}) ?

The derivative of ((x^{1/2}/(sqrt(y)))^{-3/2}) is -(3(y-x\frac{dy)/(dx))}{4x^{7/4}y^{1/4}}

What is the first derivative of ((x^{1/2}/(sqrt(y)))^{-3/2}) ?

The first derivative of ((x^{1/2}/(sqrt(y)))^{-3/2}) is -(3(y-x\frac{dy)/(dx))}{4x^{7/4}y^{1/4}}

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

- \frac{3 ( y - x \frac{d y}{d x} )}{4 x ^{\frac{7}{4}} y ^{\frac{1}{4}}}

Solution steps

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

Apply the chain rule:

- \frac{3}{2 ( \frac{x ^{\frac{1}{2}}}{y} ) ^{\frac{5}{2}}} \frac{d}{d x} (\frac{x ^{\frac{1}{2}}}{y})

= - \frac{3}{2 ( \frac{x ^{\frac{1}{2}}}{y} ) ^{\frac{5}{2}}} \frac{d}{d x} (\frac{x ^{\frac{1}{2}}}{y})

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

= - \frac{3}{2 ( \frac{x ^{\frac{1}{2}}}{y} ) ^{\frac{5}{2}}} \cdot \frac{y - x \frac{d y}{d x}}{2 x ^{\frac{1}{2}} y ^{\frac{3}{2}}}

Simplify

- \frac{3}{2 ( \frac{x ^{\frac{1}{2}}}{y} ) ^{\frac{5}{2}}} \cdot \frac{y - x \frac{d y}{d x}}{2 x ^{\frac{1}{2}} y ^{\frac{3}{2}}} : - \frac{3 ( y - x \frac{d y}{d x} )}{4 x ^{\frac{7}{4}} y ^{\frac{1}{4}}}

= - \frac{3 ( y - x \frac{d y}{d x} )}{4 x ^{\frac{7}{4}} y ^{\frac{1}{4}}}

4.7 7

5375 (1 + \frac{9.5}{1200} \cdot 1)^{- 1}

(2 e^{- j^{0.3}}) (3 e^{j^{0.2}})

610 \cdot x

What is the derivative of ((x^{1/2}/(sqrt(y)))^{-3/2}) ?
The derivative of ((x^{1/2}/(sqrt(y)))^{-3/2}) is -(3(y-x\frac{dy)/(dx))}{4x^{7/4}y^{1/4}}
What is the first derivative of ((x^{1/2}/(sqrt(y)))^{-3/2}) ?
The first derivative of ((x^{1/2}/(sqrt(y)))^{-3/2}) is -(3(y-x\frac{dy)/(dx))}{4x^{7/4}y^{1/4}}