Solve 6/12*N/18

$$\frac { 6 } { 12 } \times \frac { N } { 18 }$$

Evaluate

$$\frac{N}{36}$$

Solution Steps

Reduce the fraction \frac{6}{12} to lowest terms by extracting and canceling out 6.

$$\frac{1}{2}\times \frac{N}{18}$$

Multiply \frac{1}{2} times \frac{N}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{N}{2\times 18}$$

Multiply 2 and 18 to get 36.

$$\frac{N}{36}$$

Differentiate w.r.t. N

$$\frac{1}{36} = 0.027777777777777776$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{6}{12} to lowest terms by extracting and canceling out 6.

$$\frac{\mathrm{d}}{\mathrm{d}N}(\frac{1}{2}\times \frac{N}{18})$$

Multiply \frac{1}{2} times \frac{N}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}N}(\frac{N}{2\times 18})$$

Multiply 2 and 18 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}N}(\frac{N}{36})$$

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

$$\frac{1}{36}N^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{36}N^{0}$$

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

$$\frac{1}{36}\times 1$$

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

$$\frac{1}{36}$$