What is (\partial)/(\partial x)((1/12)pix^2y) ?

The answer to (\partial)/(\partial x)((1/12)pix^2y) is (pixy)/6

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(\partial)/(\partial x)((1/12)pix^2y)

\frac{\partial}{\partial x} ((\frac{1}{12}) π x^{2} y)

\frac{π x y}{6}

Solution steps

\frac{\partial}{\partial x} ((\frac{1}{12}) π x^{2} y)

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{12} π y \frac{\partial}{\partial x} (x^{2})

Apply the Power Rule:

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

= \frac{1}{12} π y \cdot 2 x^{2 - 1}

Simplify

\frac{1}{12} π y \cdot 2 x^{2 - 1} : \frac{π x y}{6}

= \frac{π x y}{6}

\int \frac{1}{( 25 - x ^{2} ) ^{\frac{3}{2}}} d x

\int \frac{2 x - 3}{x ^{2} 6 x ^{13}} d x

\int \frac{e ^{2 x}}{e ^{x} + 1} d x

x \to 0 lim (\frac{( x + 2 ) ^{2} - 8}{x})

x^{2} + 8 x - 3, - x^{2} + 4 x + 3

What is (\partial)/(\partial x)((1/12)pix^2y) ?
The answer to (\partial)/(\partial x)((1/12)pix^2y) is (pixy)/6