Solve (3.9*10^5)/(7.8*10^8)*H

$$\frac { ( 3.9 \times 10 ^ { 5 } ) } { ( 7.8 \times 10 ^ { 8 } ) } \cdot H$$

Evaluate

$$\frac{H}{2000}$$

Solution Steps

Cancel out 10^{5} in both numerator and denominator.

$$\frac{3.9}{7.8\times 10^{3}}H$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{3.9}{7.8\times 1000}H$$

Multiply 7.8 and 1000 to get 7800.

$$\frac{3.9}{7800}H$$

Expand \frac{3.9}{7800} by multiplying both numerator and the denominator by 10.

$$\frac{39}{78000}H$$

Reduce the fraction \frac{39}{78000} to lowest terms by extracting and canceling out 39.

$$\frac{1}{2000}H$$

Differentiate w.r.t. H

$$0.0005$$

Steps Using Definition of a Derivative

Cancel out 10^{5} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}H}(\frac{3.9}{7.8\times 10^{3}}H)$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{\mathrm{d}}{\mathrm{d}H}(\frac{3.9}{7.8\times 1000}H)$$

Multiply 7.8 and 1000 to get 7800.

$$\frac{\mathrm{d}}{\mathrm{d}H}(\frac{3.9}{7800}H)$$

Expand \frac{3.9}{7800} by multiplying both numerator and the denominator by 10.

$$\frac{\mathrm{d}}{\mathrm{d}H}(\frac{39}{78000}H)$$

Reduce the fraction \frac{39}{78000} to lowest terms by extracting and canceling out 39.

$$\frac{\mathrm{d}}{\mathrm{d}H}(\frac{1}{2000}H)$$

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

$$\frac{1}{2000}H^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{2000}H^{0}$$

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

$$\frac{1}{2000}\times 1$$

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

$$\frac{1}{2000}$$