Solve 5n^2/3n^2*3/n

$$\frac { 5 n ^ { 2 } } { 3 n ^ { 2 } } \cdot \frac { 3 } { n }$$

Evaluate

$$\frac{5}{n}$$

Solution Steps

Cancel out n^{2} in both numerator and denominator.

$$\frac{5}{3}\times \frac{3}{n}$$

Multiply \frac{5}{3} times \frac{3}{n} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 3}{3n}$$

Cancel out 3 in both numerator and denominator.

$$\frac{5}{n}$$

Differentiate w.r.t. n

$$-\frac{5}{n^{2}}$$

Steps Using Definition of a Derivative

Cancel out n^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{5}{3}\times \frac{3}{n})$$

Multiply \frac{5}{3} times \frac{3}{n} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{5\times 3}{3n})$$

Cancel out 3 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{5}{n})$$

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

$$-5n^{-1-1}$$

Subtract 1 from -1.

$$-5n^{-2}$$