Solve 8.1*10^-5m

$$8.1 \times 10 ^ { - 5 } m$$

Evaluate

$$\frac{81m}{1000000}$$

Solution Steps

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

$$8.1\times \frac{1}{100000}m$$

Multiply 8.1 and \frac{1}{100000} to get \frac{81}{1000000}.

$$\frac{81}{1000000}m$$

Differentiate w.r.t. m

$$0.000081$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(8.1\times \frac{1}{100000}m)$$

Multiply 8.1 and \frac{1}{100000} to get \frac{81}{1000000}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{81}{1000000}m)$$

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

$$\frac{81}{1000000}m^{1-1}$$

Subtract 1 from 1.

$$\frac{81}{1000000}m^{0}$$

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

$$\frac{81}{1000000}\times 1$$

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

$$\frac{81}{1000000}$$