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

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

Evaluate

$$\frac{3x^{2}}{2}$$

Solution Steps

Divide 2x^{2} by 4 to get \frac{1}{2}x^{2}.

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

Combine 2x^{2} and -\frac{1}{2}x^{2} to get \frac{3}{2}x^{2}.

$$\frac{3}{2}x^{2}$$

Differentiate w.r.t. x

$$3x$$

Steps Using Definition of a Derivative

Divide 2x^{2} by 4 to get \frac{1}{2}x^{2}.

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

Combine 2x^{2} and -\frac{1}{2}x^{2} to get \frac{3}{2}x^{2}.

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

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

$$2\times \frac{3}{2}x^{2-1}$$

Multiply 2 times \frac{3}{2}.

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

Subtract 1 from 2.

$$3x^{1}$$

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

$$3x$$