Solve y/8div3/2

$$\frac { y } { 8 } \div \frac { 3 } { 2 }$$

Evaluate

$$\frac{y}{12}$$

Solution Steps

Divide \frac{y}{8} by \frac{3}{2} by multiplying \frac{y}{8} by the reciprocal of \frac{3}{2}.

$$\frac{y\times 2}{8\times 3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{y}{3\times 4}$$

Multiply 3 and 4 to get 12.

$$\frac{y}{12}$$

Differentiate w.r.t. y

$$\frac{1}{12} = 0.08333333333333333$$

Steps Using Definition of a Derivative

Divide \frac{y}{8} by \frac{3}{2} by multiplying \frac{y}{8} by the reciprocal of \frac{3}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y\times 2}{8\times 3})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y}{3\times 4})$$

Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y}{12})$$

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

$$\frac{1}{12}y^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{12}y^{0}$$

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

$$\frac{1}{12}\times 1$$

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

$$\frac{1}{12}$$