Solve (6r^3)(2r^-4)

$$( 6 r ^ { 3 } ) ( 2 r ^ { - 4 } )$$

Evaluate

$$\frac{12}{r}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -4 to get -1.

$$6r^{-1}\times 2$$

Multiply 6 and 2 to get 12.

$$12r^{-1}$$

Differentiate w.r.t. r

$$-\frac{12}{r^{2}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and -4 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}r}(6r^{-1}\times 2)$$

Multiply 6 and 2 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}r}(12r^{-1})$$

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

$$-12r^{-1-1}$$

Subtract 1 from -1.

$$-12r^{-2}$$