Solve 10*10^-6m^2

$$10 \cdot 10 ^ { - 6 } m ^ { 2 }$$

Evaluate

$$\frac{m^{2}}{100000}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -6 to get -5.

$$10^{-5}m^{2}$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$\frac{1}{100000}m^{2}$$

Differentiate w.r.t. m

$$\frac{m}{50000}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and -6 to get -5.

$$\frac{\mathrm{d}}{\mathrm{d}m}(10^{-5}m^{2})$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{1}{100000}m^{2})$$

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

$$2\times \frac{1}{100000}m^{2-1}$$

Multiply 2 times \frac{1}{100000}.

$$\frac{1}{50000}m^{2-1}$$

Subtract 1 from 2.

$$\frac{1}{50000}m^{1}$$

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

$$\frac{1}{50000}m$$