Solve 1/2a+2a-8/4a

$$\frac{ 1 }{ 2 } a+2a- \frac{ 8 }{ 4 } a$$

Evaluate

$$\frac{a}{2}$$

Solution Steps

Combine \frac{1}{2}a and 2a to get \frac{5}{2}a.

$$\frac{5}{2}a-\frac{8}{4}a$$

Divide 8 by 4 to get 2.

$$\frac{5}{2}a-2a$$

Combine \frac{5}{2}a and -2a to get \frac{1}{2}a.

$$\frac{1}{2}a$$

Differentiate w.r.t. a

$$\frac{1}{2} = 0.5$$

Steps Using Definition of a Derivative

Combine \frac{1}{2}a and 2a to get \frac{5}{2}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5}{2}a-\frac{8}{4}a)$$

Divide 8 by 4 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5}{2}a-2a)$$

Combine \frac{5}{2}a and -2a to get \frac{1}{2}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{2}a)$$

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

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

Subtract 1 from 1.

$$\frac{1}{2}a^{0}$$

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

$$\frac{1}{2}\times 1$$

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

$$\frac{1}{2}$$