Solve 8N/1*10^4

$$\frac { 8 N } { 1 \times 10 ^ { 4 } }$$

Evaluate

$$\frac{N}{1250}$$

Solution Steps

Calculate 10 to the power of 4 and get 10000.

$$\frac{8N}{1\times 10000}$$

Multiply 1 and 10000 to get 10000.

$$\frac{8N}{10000}$$

Divide 8N by 10000 to get \frac{1}{1250}N.

$$\frac{1}{1250}N$$

Differentiate w.r.t. N

$$\frac{1}{1250} = 0.0008$$

Steps Using Definition of a Derivative

Calculate 10 to the power of 4 and get 10000.

$$\frac{\mathrm{d}}{\mathrm{d}N}(\frac{8N}{1\times 10000})$$

Multiply 1 and 10000 to get 10000.

$$\frac{\mathrm{d}}{\mathrm{d}N}(\frac{8N}{10000})$$

Divide 8N by 10000 to get \frac{1}{1250}N.

$$\frac{\mathrm{d}}{\mathrm{d}N}(\frac{1}{1250}N)$$

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

$$\frac{1}{1250}N^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{1250}N^{0}$$

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

$$\frac{1}{1250}\times 1$$

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

$$\frac{1}{1250}$$