What is the d/(dh)(pi/3 h^2(3r-h)) ?

The d/(dh)(pi/3 h^2(3r-h)) is pih(2{r}-h)

What is the first d/(dh)(pi/3 h^2(3r-h)) ?

The first d/(dh)(pi/3 h^2(3r-h)) is pih(2{r}-h)

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\frac{d}{d h} (\frac{π}{3} h^{2} (3 r - h))

πh (2 r - h)

Solution steps

\frac{d}{d h} (\frac{π}{3} h^{2} (3 r - h))

Take the constant out:

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

= \frac{π}{3} \frac{d}{d h} (h^{2} (3 r - h))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = h^{2}, g = 3 r - h

= \frac{π}{3} (\frac{d}{d h} (h^{2}) (3 r - h) + \frac{d}{d h} (3 r - h) h^{2})

\frac{d}{d h} (h^{2}) = 2 h

\frac{d}{d h} (3 r - h) = - 1

= \frac{π}{3} (2 h (3 r - h) + (- 1) h^{2})

Simplify

\frac{π}{3} (2 h (3 r - h) + (- 1) h^{2}) : πh (2 r - h)

= πh (2 r - h)

\frac{d}{d y} (e^{- y^{2}})

\frac{d}{d x} (\frac{x ^{2} - x + 1}{x ^{2} + x + 1})

x^{3} - 6 x^{2} + 5 x

\int \frac{1}{2 x - 4} d x

\frac{\partial}{\partial x} (x t)

What is the d/(dh)(pi/3 h^2(3r-h)) ?
The d/(dh)(pi/3 h^2(3r-h)) is pih(2{r}-h)
What is the first d/(dh)(pi/3 h^2(3r-h)) ?
The first d/(dh)(pi/3 h^2(3r-h)) is pih(2{r}-h)