Solve 12+32p^2+35p^3

$$12 + 32 p ^ { 2 } + 35 p ^ { 3 }$$

Differentiate w.r.t. p

$$p\left(105p+64\right)$$

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}.

$$2\times 32p^{2-1}+3\times 35p^{3-1}$$

Multiply 2 times 32.

$$64p^{2-1}+3\times 35p^{3-1}$$

Subtract 1 from 2.

$$64p^{1}+3\times 35p^{3-1}$$

Multiply 3 times 35.

$$64p^{1}+105p^{3-1}$$

Subtract 1 from 3.

$$64p^{1}+105p^{2}$$

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

$$64p+105p^{2}$$

Evaluate

$$35p^{3}+32p^{2}+12$$