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

The answer to (\partial)/(\partial x)(y^2sqrt(x)) is (y^2)/(2sqrt(x))

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(\partial)/(\partial x)(y^2sqrt(x))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply radical rule:

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

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

Simplify

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

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

\frac{\partial}{\partial x} (cos (y) - sin (x))

\int 2 (x - 3)^{3} d x

\frac{d ^{2} y}{d x ^{2}} + 4 y = sin (2)

\int x e^{y^{3}} d y

P = x^{3} - 5 x, (1, - 4)

What is (\partial)/(\partial x)(y^2sqrt(x)) ?
The answer to (\partial)/(\partial x)(y^2sqrt(x)) is (y^2)/(2sqrt(x))