Solve 21p^3+6p^2+p-4

$$21 p ^ { 3 } + 6 p ^ { 2 } + p - 4$$

Differentiate w.r.t. p

$$63p^{2}+12p+1$$

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}.

$$3\times 21p^{3-1}+2\times 6p^{2-1}+p^{1-1}$$

Multiply 3 times 21.

$$63p^{3-1}+2\times 6p^{2-1}+p^{1-1}$$

Subtract 1 from 3.

$$63p^{2}+2\times 6p^{2-1}+p^{1-1}$$

Multiply 2 times 6.

$$63p^{2}+12p^{2-1}+p^{1-1}$$

Subtract 1 from 2.

$$63p^{2}+12p^{1}+p^{1-1}$$

Subtract 1 from 1.

$$63p^{2}+12p^{1}+p^{0}$$

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

$$63p^{2}+12p+p^{0}$$

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

$$63p^{2}+12p+1$$

Evaluate

$$21p^{3}+6p^{2}+p-4$$