Solve 2/4:4/alpha

$$\frac { 2 } { 4 } : \frac { 4 } { \alpha }$$

Evaluate

$$\frac{\alpha }{8}$$

Solution Steps

Divide \frac{2}{4} by \frac{4}{\alpha } by multiplying \frac{2}{4} by the reciprocal of \frac{4}{\alpha }.

$$\frac{2\alpha }{4\times 4}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\alpha }{2\times 4}$$

Multiply 2 and 4 to get 8.

$$\frac{\alpha }{8}$$

Differentiate w.r.t. α

$$\frac{1}{8} = 0.125$$

Steps Using Definition of a Derivative

Divide \frac{2}{4} by \frac{4}{\alpha } by multiplying \frac{2}{4} by the reciprocal of \frac{4}{\alpha }.

$$\frac{\mathrm{d}}{\mathrm{d}\alpha }(\frac{2\alpha }{4\times 4})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}\alpha }(\frac{\alpha }{2\times 4})$$

Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}\alpha }(\frac{\alpha }{8})$$

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

$$\frac{1}{8}\alpha ^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{8}\alpha ^{0}$$

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

$$\frac{1}{8}\times 1$$

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

$$\frac{1}{8}$$