Solve p^3+5p^2+6p+15

$$p ^ { 3 } + 5 p ^ { 2 } + 6 p + 15$$

Differentiate w.r.t. p

$$3p^{2}+10p+6$$

Steps Using Derivative Rule for Sum

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}.

$$3p^{3-1}+2\times 5p^{2-1}+6p^{1-1}$$

Subtract 1 from 3.

$$3p^{2}+2\times 5p^{2-1}+6p^{1-1}$$

Multiply 2 times 5.

$$3p^{2}+10p^{2-1}+6p^{1-1}$$

Subtract 1 from 2.

$$3p^{2}+10p^{1}+6p^{1-1}$$

Subtract 1 from 1.

$$3p^{2}+10p^{1}+6p^{0}$$

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

$$3p^{2}+10p+6p^{0}$$

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

$$3p^{2}+10p+6\times 1$$

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

$$3p^{2}+10p+6$$

Evaluate

$$p^{3}+5p^{2}+6p+15$$