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Popular >

d/(dt)(({r}(t))/t)

Solution

\frac{d}{d t} (\frac{r ( t )}{t})

Solution

\frac{t \frac{d}{d t} ( r ( t ) ) - r ( t )}{t ^{2}}

Solution steps

\frac{d}{d t} (\frac{r ( t )}{t})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d t}{d t} = 1

= \frac{\frac{d}{d t} ( r ( t ) ) t - 1 \cdot r ( t )}{t ^{2}}

Simplify

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

Popular Examples

limit as t approaches 0 of 2/t-2/(t^2-t)

t \to 0 lim (\frac{2}{t} - \frac{2}{t ^{2} - t})

derivative of y=sin(pi-x)derivative of

y = sin (π - x)

integral from 4 to 8 of y/(y^2-2y-3)

\int_{4}^{8} \frac{y}{y ^{2} - 2 y - 3} d y

area x^3-2x^2+3,3x^2+5x-22 area

x^{3} - 2 x^{2} + 3, 3 x^{2} + 5 x - 22

integral of-e^{6t}

\int - e^{6 t} d t

Frequently Asked Questions (FAQ)

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