Solve 10:20y30:60

$$10 : 20 y 30 : 60$$

Evaluate

$$\frac{y_{30}}{120}$$

Solution Steps

Reduce the fraction \frac{10}{20} to lowest terms by extracting and canceling out 10.

$$\frac{\frac{1}{2}y_{30}}{60}$$

Divide \frac{1}{2}y_{30} by 60 to get \frac{1}{120}y_{30}.

$$\frac{1}{120}y_{30}$$

Differentiate w.r.t. y_30

$$\frac{1}{120} = 0.008333333333333333$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{10}{20} to lowest terms by extracting and canceling out 10.

$$\frac{\mathrm{d}}{\mathrm{d}y_{30}}(\frac{\frac{1}{2}y_{30}}{60})$$

Divide \frac{1}{2}y_{30} by 60 to get \frac{1}{120}y_{30}.

$$\frac{\mathrm{d}}{\mathrm{d}y_{30}}(\frac{1}{120}y_{30})$$

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

$$\frac{1}{120}y_{30}^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{120}y_{30}^{0}$$

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

$$\frac{1}{120}\times 1$$

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

$$\frac{1}{120}$$