Solve P^2-p^2-2p^2+3p^2

$$P ^ { 2 } - p ^ { 2 } - 2 p ^ { 2 } + 3 p ^ { 2 }$$

Evaluate

$$P^{2}$$

Solution Steps

Combine -p^{2} and -2p^{2} to get -3p^{2}.

$$P^{2}-3p^{2}+3p^{2}$$

Combine -3p^{2} and 3p^{2} to get 0.

$$P^{2}$$

Differentiate w.r.t. P

$$2P$$

Steps Using Definition of a Derivative

Combine -p^{2} and -2p^{2} to get -3p^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}P}(P^{2}-3p^{2}+3p^{2})$$

Combine -3p^{2} and 3p^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}P}(P^{2})$$

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

$$2P^{2-1}$$

Subtract 1 from 2.

$$2P^{1}$$

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

$$2P$$