Solve p(p^4)^3

$$p ( p ^ { 4 } ) ^ { 3 }$$

Evaluate

$$p^{13}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$pp^{12}$$

To multiply powers of the same base, add their exponents. Add 1 and 12 to get 13.

$$p^{13}$$

Differentiate w.r.t. p

$$13p^{12}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}p}(pp^{12})$$

To multiply powers of the same base, add their exponents. Add 1 and 12 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p^{13})$$

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

$$13p^{13-1}$$

Subtract 1 from 13.

$$13p^{12}$$