Solve (6p^3-8p^2+7p)+(p^2-8-8p)

$$( 6 p ^ { 3 } - 8 p ^ { 2 } + 7 p ) + ( p ^ { 2 } - 8 - 8 p )$$

Evaluate

$$6p^{3}-7p^{2}-p-8$$

Solution Steps

Combine -8p^{2} and p^{2} to get -7p^{2}.

$$6p^{3}-7p^{2}+7p-8-8p$$

Combine 7p and -8p to get -p.

$$6p^{3}-7p^{2}-p-8$$

Differentiate w.r.t. p

$$18p^{2}-14p-1$$

Steps Using Derivative Rule for Sum

Combine -8p^{2} and p^{2} to get -7p^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}p}(6p^{3}-7p^{2}+7p-8-8p)$$

Combine 7p and -8p to get -p.

$$\frac{\mathrm{d}}{\mathrm{d}p}(6p^{3}-7p^{2}-p-8)$$

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}.

$$3\times 6p^{3-1}+2\left(-7\right)p^{2-1}-p^{1-1}$$

Multiply 3 times 6.

$$18p^{3-1}+2\left(-7\right)p^{2-1}-p^{1-1}$$

Subtract 1 from 3.

$$18p^{2}+2\left(-7\right)p^{2-1}-p^{1-1}$$

Multiply 2 times -7.

$$18p^{2}-14p^{2-1}-p^{1-1}$$

Subtract 1 from 2.

$$18p^{2}-14p^{1}-p^{1-1}$$

Subtract 1 from 1.

$$18p^{2}-14p^{1}-p^{0}$$

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

$$18p^{2}-14p-p^{0}$$

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

$$18p^{2}-14p-1$$