Solve 6*10^-3N/2.7

$$\frac { 6 \times 10 ^ { - 3 } N } { 2.7 }$$

Evaluate

$$\frac{N}{450}$$

Solution Steps

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{6\times \frac{1}{1000}N}{2.7}$$

Multiply 6 and \frac{1}{1000} to get \frac{3}{500}.

$$\frac{\frac{3}{500}N}{2.7}$$

Divide \frac{3}{500}N by 2.7 to get \frac{1}{450}N.

$$\frac{1}{450}N$$

Differentiate w.r.t. N

$$\frac{1}{450} = 0.0022222222222222222$$

Steps Using Definition of a Derivative

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{\mathrm{d}}{\mathrm{d}N}(\frac{6\times \frac{1}{1000}N}{2.7})$$

Multiply 6 and \frac{1}{1000} to get \frac{3}{500}.

$$\frac{\mathrm{d}}{\mathrm{d}N}(\frac{\frac{3}{500}N}{2.7})$$

Divide \frac{3}{500}N by 2.7 to get \frac{1}{450}N.

$$\frac{\mathrm{d}}{\mathrm{d}N}(\frac{1}{450}N)$$

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

$$\frac{1}{450}N^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{450}N^{0}$$

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

$$\frac{1}{450}\times 1$$

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

$$\frac{1}{450}$$