Solve 4c^4/2c^2*c

$$\frac { 4 c ^ { 4 } } { 2 c ^ { 2 } \times c }$$

Evaluate

$$2c$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{4c^{4}}{2c^{3}}$$

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

$$2c$$

Differentiate w.r.t. c

$$2$$

Solution Steps

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

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

Do the arithmetic.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times \frac{2}{c}c^{2-1}$$

Do the arithmetic.

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

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

$$\frac{4}{c}c$$