Solve =0.1m/180*10

$$= \frac { 0.1 m } { 180 \times 10 }$$

Evaluate

$$\frac{m}{18000}$$

Solution Steps

Multiply 180 and 10 to get 1800.

$$\frac{0.1m}{1800}$$

Divide 0.1m by 1800 to get \frac{1}{18000}m.

$$\frac{1}{18000}m$$

Differentiate w.r.t. m

$$\frac{1}{18000} = 5.555555555555555 \times 10^{-5}$$

Steps Using Definition of a Derivative

Multiply 180 and 10 to get 1800.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{0.1m}{1800})$$

Divide 0.1m by 1800 to get \frac{1}{18000}m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1}{18000}m)$$

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

$$\frac{1}{18000}m^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{18000}m^{0}$$

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

$$\frac{1}{18000}\times 1$$

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

$$\frac{1}{18000}$$