Solve =4nc^3/4nc

$$= \frac { 4 n c ^ { 3 } } { 4 n c }$$

Evaluate

$$c^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{4^{1}n^{1}c^{3}}{4^{1}n^{1}c^{1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$4^{1-1}n^{1-1}c^{3-1}$$

Subtract 1 from 1.

$$4^{0}n^{1-1}c^{3-1}$$

For any number a except 0, a^{0}=1.

$$n^{1-1}c^{3-1}$$

Subtract 1 from 1.

$$n^{0}c^{3-1}$$

For any number a except 0, a^{0}=1.

$$c^{3-1}$$

Subtract 1 from 3.

$$n^{0}c^{2}$$

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

$$1c^{2}$$

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

$$c^{2}$$

Differentiate w.r.t. c

$$2c$$

Steps Using Definition of a Derivative

Cancel out 4cn in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c^{2})$$

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

$$2c^{2-1}$$

Subtract 1 from 2.

$$2c^{1}$$

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

$$2c$$