Solve p^8(-p^6)p^6

$$p ^ { 8 } ( - p ^ { 6 } ) p ^ { 6 }$$

Evaluate

$$-p^{20}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 6 to get 14.

$$p^{14}\left(-p^{6}\right)$$

To multiply powers of the same base, add their exponents. Add 14 and 6 to get 20.

$$p^{20}\left(-1\right)$$

Differentiate w.r.t. p

$$-20p^{19}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 8 and 6 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p^{14}\left(-p^{6}\right))$$

To multiply powers of the same base, add their exponents. Add 14 and 6 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p^{20}\left(-1\right))$$

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

$$20\left(-1\right)p^{20-1}$$

Multiply 20 times -1.

$$-20p^{20-1}$$

Subtract 1 from 20.

$$-20p^{19}$$