Solve 3p^2*4p^5

$$3 p ^ { 2 } \times 4 p ^ { 5 }$$

Evaluate

$$12p^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$3p^{7}\times 4$$

Multiply 3 and 4 to get 12.

$$12p^{7}$$

Differentiate w.r.t. p

$$84p^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}p}(3p^{7}\times 4)$$

Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}p}(12p^{7})$$

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

$$7\times 12p^{7-1}$$

Multiply 7 times 12.

$$84p^{7-1}$$

Subtract 1 from 7.

$$84p^{6}$$