What is (\partial)/(\partial x)(4/3 pix^3) ?

The answer to (\partial)/(\partial x)(4/3 pix^3) is 4pix^2

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(\partial)/(\partial x)(4/3 pix^3)

\frac{\partial}{\partial x} (\frac{4}{3} π x^{3})

4 π x^{2}

Solution steps

\frac{\partial}{\partial x} (\frac{4}{3} π x^{3})

Take the constant out:

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

= \frac{4}{3} π \frac{\partial}{\partial x} (x^{3})

Apply the Power Rule:

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

= \frac{4}{3} π 3 x^{3 - 1}

Simplify

\frac{4}{3} π 3 x^{3 - 1} : 4 π x^{2}

= 4 π x^{2}

\frac{\partial}{\partial x} ((x^{4} + 3 x^{2}) (1 - 5 x))

y^{^{''}} - 6 y^{^{'}} + 8 y = 0, y (0) = 2, y^{^{'}} (0) = 1

x \to - 1 - lim (\frac{x}{x + 1})

\int \frac{5 x + 4}{x ^{3}} d x

\int e^{x^{3} - 3 x^{2}} d y

What is (\partial)/(\partial x)(4/3 pix^3) ?
The answer to (\partial)/(\partial x)(4/3 pix^3) is 4pix^2