Solve 3c^6*2c/4c^2

$$\frac { 3 c ^ { 6 } \times 2 c } { 4 c ^ { 2 } }$$

Evaluate

$$\frac{3c^{5}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{3c^{7}\times 2}{4c^{2}}$$

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

$$\frac{3c^{5}}{2}$$

Differentiate w.r.t. c

$$\frac{15c^{4}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{6c}{4}c^{6-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{3c}{2}c^{4})$$

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}.

$$4\times \frac{3c}{2}c^{4-1}$$

Do the arithmetic.

$$6cc^{3}$$