Solve (3p^2-2p+3)+(p^2-7p+7)

$$( 3 p ^ { 2 } - 2 p + 3 ) + ( p ^ { 2 } - 7 p + 7 )$$

Evaluate

$$4p^{2}-9p+10$$

Solution Steps

Combine 3p^{2} and p^{2} to get 4p^{2}.

$$4p^{2}-2p+3-7p+7$$

Combine -2p and -7p to get -9p.

$$4p^{2}-9p+3+7$$

Add 3 and 7 to get 10.

$$4p^{2}-9p+10$$

Differentiate w.r.t. p

$$8p-9$$

Steps Using Derivative Rule for Sum

Combine 3p^{2} and p^{2} to get 4p^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}p}(4p^{2}-2p+3-7p+7)$$

Combine -2p and -7p to get -9p.

$$\frac{\mathrm{d}}{\mathrm{d}p}(4p^{2}-9p+3+7)$$

Add 3 and 7 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}p}(4p^{2}-9p+10)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times 4p^{2-1}-9p^{1-1}$$

Multiply 2 times 4.

$$8p^{2-1}-9p^{1-1}$$

Subtract 1 from 2.

$$8p^{1}-9p^{1-1}$$

Subtract 1 from 1.

$$8p^{1}-9p^{0}$$

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

$$8p-9p^{0}$$

For any term t except 0, t^{0}=1.

$$8p-9$$