Solve 2x^3+43x^2+118x+32

$$2 { x }^{ 3 } +43 { x }^{ 2 } +118x+32$$

Differentiate w.r.t. x

$$6x^{2}+86x+118$$

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}.

$$3\times 2x^{3-1}+2\times 43x^{2-1}+118x^{1-1}$$

Multiply 3 times 2.

$$6x^{3-1}+2\times 43x^{2-1}+118x^{1-1}$$

Subtract 1 from 3.

$$6x^{2}+2\times 43x^{2-1}+118x^{1-1}$$

Multiply 2 times 43.

$$6x^{2}+86x^{2-1}+118x^{1-1}$$

Subtract 1 from 2.

$$6x^{2}+86x^{1}+118x^{1-1}$$

Subtract 1 from 1.

$$6x^{2}+86x^{1}+118x^{0}$$

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

$$6x^{2}+86x+118x^{0}$$

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

$$6x^{2}+86x+118\times 1$$

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

$$6x^{2}+86x+118$$

Evaluate

$$2x^{3}+43x^{2}+118x+32$$