Solve 5p^2*2p^3

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

Evaluate

$$10p^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

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

Multiply 5 and 2 to get 10.

$$10p^{5}$$

Differentiate w.r.t. p

$$50p^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}p}(5p^{5}\times 2)$$

Multiply 5 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}p}(10p^{5})$$

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

$$5\times 10p^{5-1}$$

Multiply 5 times 10.

$$50p^{5-1}$$

Subtract 1 from 5.

$$50p^{4}$$