Solve xxx-3x+3

$$xxx-3x+3$$

Evaluate

$$x^{3}-3x+3$$

Solution Steps

Multiply x and x to get x^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{3}-3x+3$$

Differentiate w.r.t. x

$$3\left(x^{2}-1\right)$$

Steps Using Derivative Rule for Sum

Multiply x and x to get x^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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}.

$$3x^{3-1}-3x^{1-1}$$

Subtract 1 from 3.

$$3x^{2}-3x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}-3x^{0}$$

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

$$3x^{2}-3$$