What is (\partial)/(\partial x)(x^2y^{0.5}) ?

The answer to (\partial)/(\partial x)(x^2y^{0.5}) is 2xy^{1/2}

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(\partial)/(\partial x)(x^2y^{0.5})

\frac{\partial}{\partial x} (x^{2} y^{0.5})

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

Solution steps

\frac{\partial}{\partial x} (x^{2} y^{0.5})

Treat

y

as a constant

Take the constant out:

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

= y^{0.5} \frac{\partial}{\partial x} (x^{2})

Apply the Power Rule:

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

= y^{0.5} \cdot 2 x^{2 - 1}

Simplify

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

\int \frac{e ^{6 s i n (x)}}{sec ( x )} d x

\frac{d}{d x} (ln (csc (x)))

\frac{d}{d t} (ln (t^{2}))

\frac{d}{d x} (x^{\frac{3}{4}} - 2 x^{\frac{1}{4}})

\frac{\partial}{\partial x} (\frac{4 y}{x})

What is (\partial)/(\partial x)(x^2y^{0.5}) ?
The answer to (\partial)/(\partial x)(x^2y^{0.5}) is 2xy^{1/2}