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

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

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

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

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\frac{d}{d t} (π r (t) (t)^{2} h)

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

Solution steps

\frac{d}{d t} (π r (t) (t)^{2} h)

Take the constant out:

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

= 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}

= 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

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

\int (x + 1)^{2} e^{x} d x

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

\frac{d}{d x} (ln (ln (x^{2 x})))

\int \frac{27}{x ( x ^{2} + 4 ) ^{2}} d x

\frac{d y}{d x} = ln (x^{y})

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