Solve -6k^6div3k^3

$$- 6 k ^ { 6 } \div 3 k ^ { 3 }$$

Evaluate

$$-2k^{9}$$

Solution Steps

Divide -6k^{6} by 3 to get -2k^{6}.

$$-2k^{6}k^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$-2k^{9}$$

Differentiate w.r.t. k

$$-18k^{8}$$

Steps Using Definition of a Derivative

Divide -6k^{6} by 3 to get -2k^{6}.

$$\frac{\mathrm{d}}{\mathrm{d}k}(-2k^{6}k^{3})$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}k}(-2k^{9})$$

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

$$9\left(-2\right)k^{9-1}$$

Multiply 9 times -2.

$$-18k^{9-1}$$

Subtract 1 from 9.

$$-18k^{8}$$