Solve 0.51*10^-6m/2897.8

$$\frac { 0.51 \times 10 ^ { - 6 } m } { 2897.8 }$$

Evaluate

$$\frac{51m}{289780000000}$$

Solution Steps

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{0.51\times \frac{1}{1000000}m}{2897.8}$$

Multiply 0.51 and \frac{1}{1000000} to get \frac{51}{100000000}.

$$\frac{\frac{51}{100000000}m}{2897.8}$$

Divide \frac{51}{100000000}m by 2897.8 to get \frac{51}{289780000000}m.

$$\frac{51}{289780000000}m$$

Differentiate w.r.t. m

$$\frac{51}{289780000000} = 1.7599558285595966 \times 10^{-10}$$

Steps Using Definition of a Derivative

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{0.51\times \frac{1}{1000000}m}{2897.8})$$

Multiply 0.51 and \frac{1}{1000000} to get \frac{51}{100000000}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{\frac{51}{100000000}m}{2897.8})$$

Divide \frac{51}{100000000}m by 2897.8 to get \frac{51}{289780000000}m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{51}{289780000000}m)$$

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

$$\frac{51}{289780000000}m^{1-1}$$

Subtract 1 from 1.

$$\frac{51}{289780000000}m^{0}$$

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

$$\frac{51}{289780000000}\times 1$$

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

$$\frac{51}{289780000000}$$