Solve {l}{x^2-x^2+}{+2x-}{-2x}

$$\left. \begin{array} { l } { x ^ { 2 } - x ^ { 2 } + } \\ { + 2 x - } \\ { - 2 x } \end{array} \right.$$

Evaluate

$$4x$$

Solution Steps

Combine x^{2} and -x^{2} to get 0.

$$2x-\left(-2x\right)$$

The opposite of -2x is 2x.

$$2x+2x$$

Combine 2x and 2x to get 4x.

$$4x$$

Differentiate w.r.t. x

$$4$$

Steps Using Definition of a Derivative

Combine x^{2} and -x^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x-\left(-2x\right))$$

The opposite of -2x is 2x.

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

Combine 2x and 2x to get 4x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x)$$

The derivative of ax^{n} is nax^{n-1}.

$$4x^{1-1}$$

Subtract 1 from 1.

$$4x^{0}$$

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

$$4\times 1$$

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

$$4$$