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

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

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

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

\frac{y ^{\frac{3}{2}}}{2 x ^{\frac{1}{2}}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{y ^{\frac{3}{2}}}{2 x ^{\frac{1}{2}}}

\frac{d}{d x} (- \frac{4}{( x - 2 ) ^{2}})

y^{^{'}} = y^{3}, y (0) = a

\frac{\partial}{\partial x} (e^{x + y^{2}})

\int (x^{8} + 1) d x

\int \frac{1}{sin ^{2} ( 2 x )} d x

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