What is (\partial)/(\partial x)(4x^3y^{1/2}) ?

The answer to (\partial)/(\partial x)(4x^3y^{1/2}) is 12x^2y^{1/2}

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(\partial)/(\partial x)(4x^3y^{1/2})

\frac{\partial}{\partial x} (4 x^{3} y^{\frac{1}{2}})

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

Solution steps

\frac{\partial}{\partial x} (4 x^{3} y^{\frac{1}{2}})

Treat

y

as a constant

Take the constant out:

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

= 4 y^{\frac{1}{2}} \frac{\partial}{\partial x} (x^{3})

Apply the Power Rule:

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

= 4 y^{\frac{1}{2}} \cdot 3 x^{3 - 1}

Simplify

= 12 x^{2} y^{\frac{1}{2}}

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 5)^{6})

x \to - 1 lim (\frac{x ^{2}}{x ^{3} - x})

\frac{\partial}{\partial x} (4 y^{2} x^{3})

\int_{0}^{1} (x + 1) (x^{2} + 2 x)^{5} d x

\int \frac{- 1800 x}{25 - x ^{2}} d x

What is (\partial)/(\partial x)(4x^3y^{1/2}) ?
The answer to (\partial)/(\partial x)(4x^3y^{1/2}) is 12x^2y^{1/2}