Solve B:2:5:5:12

$$B : 2 : 5 : 5 : 12$$

Evaluate

$$\frac{B}{600}$$

Solution Steps

Express \frac{\frac{\frac{\frac{B}{2}}{5}}{5}}{12} as a single fraction.

$$\frac{\frac{\frac{B}{2}}{5}}{5\times 12}$$

Express \frac{\frac{B}{2}}{5} as a single fraction.

$$\frac{\frac{B}{2\times 5}}{5\times 12}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{B}{10}}{5\times 12}$$

Multiply 5 and 12 to get 60.

$$\frac{\frac{B}{10}}{60}$$

Express \frac{\frac{B}{10}}{60} as a single fraction.

$$\frac{B}{10\times 60}$$

Multiply 10 and 60 to get 600.

$$\frac{B}{600}$$

Differentiate w.r.t. B

$$\frac{1}{600} = 0.0016666666666666668$$

Steps Using Definition of a Derivative

Express \frac{\frac{\frac{\frac{B}{2}}{5}}{5}}{12} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}B}(\frac{\frac{\frac{B}{2}}{5}}{5\times 12})$$

Express \frac{\frac{B}{2}}{5} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}B}(\frac{\frac{B}{2\times 5}}{5\times 12})$$

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}B}(\frac{\frac{B}{10}}{5\times 12})$$

Multiply 5 and 12 to get 60.

$$\frac{\mathrm{d}}{\mathrm{d}B}(\frac{\frac{B}{10}}{60})$$

Express \frac{\frac{B}{10}}{60} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}B}(\frac{B}{10\times 60})$$

Multiply 10 and 60 to get 600.

$$\frac{\mathrm{d}}{\mathrm{d}B}(\frac{B}{600})$$

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

$$\frac{1}{600}B^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{600}B^{0}$$

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

$$\frac{1}{600}\times 1$$

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

$$\frac{1}{600}$$