Solve =10*10^-2m

$$= 10 \times 10 ^ { - 2 } m$$

Evaluate

$$\frac{m}{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$10^{-1}m$$

Calculate 10 to the power of -1 and get \frac{1}{10}.

$$\frac{1}{10}m$$

Differentiate w.r.t. m

$$\frac{1}{10} = 0.1$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}m}(10^{-1}m)$$

Calculate 10 to the power of -1 and get \frac{1}{10}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1}{10}m)$$

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

$$\frac{1}{10}m^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{10}m^{0}$$

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

$$\frac{1}{10}\times 1$$

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

$$\frac{1}{10}$$