What is (\partial)/(\partial x)(pi*(x/2)^2h) ?

The answer to (\partial)/(\partial x)(pi*(x/2)^2h) is (pihx)/2

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(\partial)/(\partial x)(pi*(x/2)^2h)

\frac{\partial}{\partial x} (π \cdot (\frac{x}{2})^{2} h)

\frac{πh x}{2}

Solution steps

\frac{\partial}{\partial x} (π (\frac{x}{2})^{2} h)

Take the constant out:

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

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

Apply the chain rule:

2 \cdot \frac{x}{2} \frac{\partial}{\partial x} (\frac{x}{2})

= 2 \cdot \frac{x}{2} \frac{\partial}{\partial x} (\frac{x}{2})

\frac{\partial}{\partial x} (\frac{x}{2}) = \frac{1}{2}

= πh \cdot 2 \cdot \frac{x}{2} \cdot \frac{1}{2}

Simplify

πh \cdot 2 \cdot \frac{x}{2} \cdot \frac{1}{2} : \frac{πh x}{2}

= \frac{πh x}{2}

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What is (\partial)/(\partial x)(pi*(x/2)^2h) ?
The answer to (\partial)/(\partial x)(pi*(x/2)^2h) is (pihx)/2