Solve p(32)quadp(56)

$$p ( 32 ) \quad p ( 56 )$$

Evaluate

$$1792p^{2}$$

Solution Steps

Multiply p and p to get p^{2}.

$$p^{2}\times 32\times 56$$

Multiply 32 and 56 to get 1792.

$$p^{2}\times 1792$$

Differentiate w.r.t. p

$$3584p$$

Steps Using Definition of a Derivative

Multiply p and p to get p^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p^{2}\times 32\times 56)$$

Multiply 32 and 56 to get 1792.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p^{2}\times 1792)$$

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

$$2\times 1792p^{2-1}$$

Multiply 2 times 1792.

$$3584p^{2-1}$$

Subtract 1 from 2.

$$3584p^{1}$$

For any term t, t^{1}=t.

$$3584p$$