What is the d/(dt)(1/3 pi{r}(t)(t)^2h) ?

The d/(dt)(1/3 pi{r}(t)(t)^2h) is (pih(t^2 d/(dt)({r}(t))+2t{r}(t)))/3

What is the first d/(dt)(1/3 pi{r}(t)(t)^2h) ?

The first d/(dt)(1/3 pi{r}(t)(t)^2h) is (pih(t^2 d/(dt)({r}(t))+2t{r}(t)))/3

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\frac{d}{d t} (\frac{1}{3} π r (t) (t)^{2} h)

\frac{πh ( t ^{2} \frac{d}{d t} ( r ( t ) ) + 2 t r ( t ) )}{3}

Solution steps

\frac{d}{d t} (\frac{1}{3} π r (t) (t)^{2} h)

Take the constant out:

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

= \frac{1}{3} πh \frac{d}{d t} (r (t) t^{2})

Apply the Product Rule:

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

f = r (t), g = t^{2}

= \frac{1}{3} πh (\frac{d}{d t} (r (t)) t^{2} + \frac{d}{d t} (t^{2}) r (t))

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

= \frac{1}{3} πh (\frac{d}{d t} (r (t)) t^{2} + 2 t r (t))

Simplify

\frac{1}{3} πh (\frac{d}{d t} (r (t)) t^{2} + 2 t r (t)) : \frac{πh ( t ^{2} \frac{d}{d t} ( r ( t ) ) + 2 t r ( t ) )}{3}

= \frac{πh ( t ^{2} \frac{d}{d t} ( r ( t ) ) + 2 t r ( t ) )}{3}

\frac{\partial}{\partial x} (\frac{7 x - 5 y}{y ^{2} + x ^{2}})

x \to - π lim ((x + π) csc (x))

8 t \frac{d y}{d t} + y = t^{7}

\frac{d}{d x} (\frac{x ^{2}}{x ^{4} + x ^{2} + 1})

\frac{d}{d x} (arcsin (sin (x) - cos (x)))

What is the d/(dt)(1/3 pi{r}(t)(t)^2h) ?
The d/(dt)(1/3 pi{r}(t)(t)^2h) is (pih(t^2 d/(dt)({r}(t))+2t{r}(t)))/3
What is the first d/(dt)(1/3 pi{r}(t)(t)^2h) ?
The first d/(dt)(1/3 pi{r}(t)(t)^2h) is (pih(t^2 d/(dt)({r}(t))+2t{r}(t)))/3