Solve =12/6.022*10^23g

$$= \frac { 12 } { 6.022 \times 10 ^ { 23 } } g$$

Evaluate

$$\frac{3g}{150550000000000000000000}$$

Solution Steps

Calculate 10 to the power of 23 and get 100000000000000000000000.

$$\frac{12}{6.022\times 100000000000000000000000}g$$

Multiply 6.022 and 100000000000000000000000 to get 602200000000000000000000.

$$\frac{12}{602200000000000000000000}g$$

Reduce the fraction \frac{12}{602200000000000000000000} to lowest terms by extracting and canceling out 4.

$$\frac{3}{150550000000000000000000}g$$

Differentiate w.r.t. g

$$\frac{3}{150550000000000000000000} = 1.9926934573231485 \times 10^{-23}$$

Steps Using Definition of a Derivative

Calculate 10 to the power of 23 and get 100000000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{12}{6.022\times 100000000000000000000000}g)$$

Multiply 6.022 and 100000000000000000000000 to get 602200000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{12}{602200000000000000000000}g)$$

Reduce the fraction \frac{12}{602200000000000000000000} to lowest terms by extracting and canceling out 4.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{3}{150550000000000000000000}g)$$

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

$$\frac{3}{150550000000000000000000}g^{1-1}$$

Subtract 1 from 1.

$$\frac{3}{150550000000000000000000}g^{0}$$

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

$$\frac{3}{150550000000000000000000}\times 1$$

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

$$\frac{3}{150550000000000000000000}$$