Solve 2m^0n^5/8n^3

$$\frac { 2 m ^ { 0 } n ^ { 5 } } { 8 n ^ { 3 } }$$

Evaluate

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

Solution Steps

Cancel out 2n^{3} in both numerator and denominator.

$$\frac{m^{0}n^{2}}{4}$$

Calculate m to the power of 0 and get 1.

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

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

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

Differentiate w.r.t. n

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

Steps Using Definition of a Derivative

Cancel out 2n^{3} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{m^{0}n^{2}}{4})$$

Calculate m to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1n^{2}}{4})$$

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.

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