Solve 7c^2x/3cydiv14xy/c^3

$$\frac { 7 c ^ { 2 } x } { 3 c y } \div \frac { 14 x y } { c ^ { 3 } }$$

Evaluate

$$\frac{c^{4}}{6y^{2}}$$

Solution Steps

Divide \frac{7c^{2}x}{3cy} by \frac{14xy}{c^{3}} by multiplying \frac{7c^{2}x}{3cy} by the reciprocal of \frac{14xy}{c^{3}}.

$$\frac{7c^{2}xc^{3}}{3cy\times 14xy}$$

Cancel out 7cx in both numerator and denominator.

$$\frac{cc^{3}}{2\times 3yy}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

Multiply y and y to get y^{2}.

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

Multiply 2 and 3 to get 6.

$$\frac{c^{4}}{6y^{2}}$$

Differentiate w.r.t. c

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