Solve x^2/4-x^2/2

$$\frac { x ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 2 }$$

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

Combine \frac{x^{2}}{4} and -\frac{x^{2}}{2} to get -\frac{1}{4}x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{1}{4}x^{2})$$

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

$$2\left(-\frac{1}{4}\right)x^{2-1}$$

Multiply 2 times -\frac{1}{4}.

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

Subtract 1 from 2.

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

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

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

Evaluate

$$-\frac{x^{2}}{4}$$

Solution Steps

Combine \frac{x^{2}}{4} and -\frac{x^{2}}{2} to get -\frac{1}{4}x^{2}.

$$-\frac{1}{4}x^{2}$$