Solve 8n^2/5mdiv2n/25m

$$\frac { 8 n ^ { 2 } } { 5 m } \div \frac { 2 n } { 25 m }$$

Evaluate

$$20n$$

Solution Steps

Divide \frac{8n^{2}}{5m} by \frac{2n}{25m} by multiplying \frac{8n^{2}}{5m} by the reciprocal of \frac{2n}{25m}.

$$\frac{8n^{2}\times 25m}{5m\times 2n}$$

Cancel out 2\times 5mn in both numerator and denominator.

$$4\times 5n$$

Multiply 4 and 5 to get 20.

$$20n$$

Differentiate w.r.t. n

$$20$$

Steps Using Definition of a Derivative

Divide \frac{8n^{2}}{5m} by \frac{2n}{25m} by multiplying \frac{8n^{2}}{5m} by the reciprocal of \frac{2n}{25m}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{8n^{2}\times 25m}{5m\times 2n})$$

Cancel out 2\times 5mn in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}n}(4\times 5n)$$

Multiply 4 and 5 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}n}(20n)$$

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

$$20n^{1-1}$$

Subtract 1 from 1.

$$20n^{0}$$

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

$$20\times 1$$

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

$$20$$