Solve 12x^3+85x^2+5

$$12 { x }^{ 3 } +85 { x }^{ 2 } +5$$

Differentiate w.r.t. x

$$2x\left(18x+85\right)$$

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}.

$$3\times 12x^{3-1}+2\times 85x^{2-1}$$

Multiply 3 times 12.

$$36x^{3-1}+2\times 85x^{2-1}$$

Subtract 1 from 3.

$$36x^{2}+2\times 85x^{2-1}$$

Multiply 2 times 85.

$$36x^{2}+170x^{2-1}$$

Subtract 1 from 2.

$$36x^{2}+170x^{1}$$

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

$$36x^{2}+170x$$

Evaluate

$$12x^{3}+85x^{2}+5$$