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

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

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(\partial)/(\partial x)(xy^{1/2})

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

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

Simplify

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

R (t) = 50 t^{2} e^{- t} + 8

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

y^{^{''}} - 8 y^{^{'}} + 16 y = t^{- 3} e^{4 t}

(16 + x^{2}) (\frac{d y}{d x}) - 2 x y = 0

ln (\frac{x ^{2}}{3 - x})

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