Solve 3n/4*(2)n/6

$$\frac { 3 n } { 4 } \cdot ( 2 ) \frac { n } { 6 }$$

Evaluate

$$\frac{n^{2}}{4}$$

Solution Steps

Cancel out 4, the greatest common factor in 2 and 4.

$$\frac{3n}{2}\times \frac{n}{6}$$

Multiply \frac{3n}{2} times \frac{n}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3nn}{2\times 6}$$

Cancel out 3 in both numerator and denominator.

$$\frac{nn}{2\times 2}$$

Multiply n and n to get n^{2}.

$$\frac{n^{2}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{n^{2}}{4}$$

Differentiate w.r.t. n

$$\frac{n}{2}$$

Steps Using Definition of a Derivative

Cancel out 4, the greatest common factor in 2 and 4.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{3n}{2}\times \frac{n}{6})$$

Multiply \frac{3n}{2} times \frac{n}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{3nn}{2\times 6})$$

Cancel out 3 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{nn}{2\times 2})$$

Multiply n and n to get n^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{n^{2}}{2\times 2})$$

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{n^{2}}{4})$$

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

$$2\times \frac{1}{4}n^{2-1}$$

Multiply 2 times \frac{1}{4}.

$$\frac{1}{2}n^{2-1}$$

Subtract 1 from 2.

$$\frac{1}{2}n^{1}$$

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

$$\frac{1}{2}n$$