Solve 5p^3*3p^5=

$$5 p ^ { 3 } \cdot 3 p ^ { 5 } =$$

Evaluate

$$15p^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$5p^{8}\times 3$$

Multiply 5 and 3 to get 15.

$$15p^{8}$$

Differentiate w.r.t. p

$$120p^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}p}(5p^{8}\times 3)$$

Multiply 5 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}p}(15p^{8})$$

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

$$8\times 15p^{8-1}$$

Multiply 8 times 15.

$$120p^{8-1}$$

Subtract 1 from 8.

$$120p^{7}$$