What is (\partial)/(\partial x)(4/3 pi(y^3-x^3)) ?

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

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(\partial)/(\partial x)(4/3 pi(y^3-x^3))

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

- 4 π x^{2}

Solution steps

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

Simplify

\frac{4}{3} π (y^{3} - x^{3}) : \frac{4 π}{3} (y^{3} - x^{3})

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (y^{3}) = 0

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

= \frac{4 π}{3} (0 - 3 x^{2})

Simplify

\frac{4 π}{3} (0 - 3 x^{2}) : - 4 π x^{2}

= - 4 π x^{2}

x^{6 c o s (x)}

e^{- 11 x}

(8 x^{2} - 5)^{\frac{1}{2}}

\int_{0}^{3} (2 x - 1) d x

\frac{\partial}{\partial z} (x^{2} + (y - 1)^{2} + z^{2})

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