Solve b/12:3/1

$$\frac { b } { 12 } : \frac { 3 } { 1 }$$

Evaluate

$$\frac{b}{36}$$

Solution Steps

Divide \frac{b}{12} by \frac{3}{1} by multiplying \frac{b}{12} by the reciprocal of \frac{3}{1}.

$$\frac{b}{12\times 3}$$

Multiply 12 and 3 to get 36.

$$\frac{b}{36}$$

Differentiate w.r.t. b

$$\frac{1}{36} = 0.027777777777777776$$

Steps Using Definition of a Derivative

Divide \frac{b}{12} by \frac{3}{1} by multiplying \frac{b}{12} by the reciprocal of \frac{3}{1}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{b}{12\times 3})$$

Multiply 12 and 3 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{b}{36})$$

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

$$\frac{1}{36}b^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{36}b^{0}$$

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

$$\frac{1}{36}\times 1$$

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

$$\frac{1}{36}$$