Solve 5(p^3)^4

$$5 ( p ^ { 3 } ) ^ { 4 }$$

Differentiate w.r.t. p

$$60p^{11}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(5p^{12})$$

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

$$12\times 5p^{12-1}$$

Multiply 12 times 5.

$$60p^{12-1}$$

Subtract 1 from 12.

$$60p^{11}$$

Evaluate

$$5p^{12}$$

Solution Steps

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

$$5p^{12}$$