Solve 2x^2+3x^2-1/2x^2=

$$2 { x }^{ 2 } +3 { x }^{ 2 } - \frac{ 1 }{ 2 } { x }^{ 2 } =$$

Evaluate

$$\frac{9x^{2}}{2}$$

Solution Steps

Combine 2x^{2} and 3x^{2} to get 5x^{2}.

$$5x^{2}-\frac{1}{2}x^{2}$$

Combine 5x^{2} and -\frac{1}{2}x^{2} to get \frac{9}{2}x^{2}.

$$\frac{9}{2}x^{2}$$

Differentiate w.r.t. x

$$9x$$

Steps Using Definition of a Derivative

Combine 2x^{2} and 3x^{2} to get 5x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}-\frac{1}{2}x^{2})$$

Combine 5x^{2} and -\frac{1}{2}x^{2} to get \frac{9}{2}x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9}{2}x^{2})$$

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

$$2\times \frac{9}{2}x^{2-1}$$

Multiply 2 times \frac{9}{2}.

$$9x^{2-1}$$

Subtract 1 from 2.

$$9x^{1}$$

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

$$9x$$