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

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

Evaluate

$$-6r^{4}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$-6r^{-2}r^{6}$$

To multiply powers of the same base, add their exponents. Add -2 and 6 to get 4.

$$-6r^{4}$$

Differentiate w.r.t. r

$$-24r^{3}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

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

To multiply powers of the same base, add their exponents. Add -2 and 6 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}r}(-6r^{4})$$

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

$$4\left(-6\right)r^{4-1}$$

Multiply 4 times -6.

$$-24r^{4-1}$$

Subtract 1 from 4.

$$-24r^{3}$$