Solve 18x^3+7x+12div3x-2

$$18 { x }^{ 3 } +7x+12 \div 3x-2$$

Evaluate

$$18x^{3}+11x-2$$

Solution Steps

Divide 12 by 3 to get 4.

$$18x^{3}+7x+4x-2$$

Combine 7x and 4x to get 11x.

$$18x^{3}+11x-2$$

Differentiate w.r.t. x

$$54x^{2}+11$$

Steps Using Derivative Rule for Sum

Divide 12 by 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{3}+7x+4x-2)$$

Combine 7x and 4x to get 11x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{3}+11x-2)$$

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}.

$$3\times 18x^{3-1}+11x^{1-1}$$

Multiply 3 times 18.

$$54x^{3-1}+11x^{1-1}$$

Subtract 1 from 3.

$$54x^{2}+11x^{1-1}$$

Subtract 1 from 1.

$$54x^{2}+11x^{0}$$

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

$$54x^{2}+11\times 1$$

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

$$54x^{2}+11$$