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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply radical rule:

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

= 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}

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

Simplify

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

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

\int e^{\frac{1}{x}} - e^{\frac{1}{x + 1}} d x

\frac{d}{d x} (ln (e^{x} - y))

\int x^{3} x^{2} - 1 d x

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

\int sin^{3} (7 x) cos^{- 2} (7 x) d x

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