Solve (-x^2/2+2x^2/2)=

$$( \frac{ - { x }^{ 2 } }{ 2 } + \frac{ 2 { x }^{ 2 } }{ 2 } )=$$

Evaluate

$$\frac{x^{2}}{2}$$

Short Solution Steps

Since \frac{-x^{2}}{2} and \frac{2x^{2}}{2} have the same denominator, add them by adding their numerators.

$$\frac{-x^{2}+2x^{2}}{2}$$

Combine like terms in -x^{2}+2x^{2}.

$$\frac{x^{2}}{2}$$

Differentiate w.r.t. x

$$x$$

Steps Using Definition of a Derivative

Since \frac{-x^{2}}{2} and \frac{2x^{2}}{2} have the same denominator, add them by adding their numerators.

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

Combine like terms in -x^{2}+2x^{2}.

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

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

$$2\times \frac{1}{2}x^{2-1}$$

Multiply 2 times \frac{1}{2}.

$$x^{2-1}$$

Subtract 1 from 2.

$$x^{1}$$

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

$$x$$