Solve r/r^-1r^-2

$$\frac { r } { r ^ { - 1 } r ^ { - 2 } }$$

Evaluate

$$r^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -1 and -2 to get -3.

$$\frac{r}{r^{-3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -3 from 1 to get 4.

$$r^{4}$$

Differentiate w.r.t. r

$$4r^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -1 and -2 to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{r}{r^{-3}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -3 from 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}r}(r^{4})$$

The derivative of ax^{n} is nax^{n-1}.

$$4r^{4-1}$$

Subtract 1 from 4.

$$4r^{3}$$