Solve (3p^2+3p-2)+(-6p^2+5p-5)

$$( 3 p ^ { 2 } + 3 p - 2 ) + ( - 6 p ^ { 2 } + 5 p - 5 )$$

Evaluate

$$-3p^{2}+8p-7$$

Solution Steps

Combine 3p^{2} and -6p^{2} to get -3p^{2}.

$$-3p^{2}+3p-2+5p-5$$

Combine 3p and 5p to get 8p.

$$-3p^{2}+8p-2-5$$

Subtract 5 from -2 to get -7.

$$-3p^{2}+8p-7$$

Differentiate w.r.t. p

$$8-6p$$

Steps Using Derivative Rule for Sum

Combine 3p^{2} and -6p^{2} to get -3p^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}p}(-3p^{2}+3p-2+5p-5)$$

Combine 3p and 5p to get 8p.

$$\frac{\mathrm{d}}{\mathrm{d}p}(-3p^{2}+8p-2-5)$$

Subtract 5 from -2 to get -7.

$$\frac{\mathrm{d}}{\mathrm{d}p}(-3p^{2}+8p-7)$$

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}.

$$2\left(-3\right)p^{2-1}+8p^{1-1}$$

Multiply 2 times -3.

$$-6p^{2-1}+8p^{1-1}$$

Subtract 1 from 2.

$$-6p^{1}+8p^{1-1}$$

Subtract 1 from 1.

$$-6p^{1}+8p^{0}$$

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

$$-6p+8p^{0}$$

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

$$-6p+8\times 1$$

For any term t, t\times 1=t and 1t=t.

$$-6p+8$$