Solve frac{8x^{3}y^{4}}{14x^2y}div6xy^3/7x^2y^2=

$$\frac { 8 x ^ { 3 } y ^ { 4 } } { 14 x ^ { 2 } y } \div \frac { 6 x y ^ { 3 } } { 7 x ^ { 2 } y ^ { 2 } } =$$

Evaluate

$$\frac{2\left(xy\right)^{2}}{3}$$

Solution Steps

Divide \frac{8x^{3}y^{4}}{14x^{2}y} by \frac{6xy^{3}}{7x^{2}y^{2}} by multiplying \frac{8x^{3}y^{4}}{14x^{2}y} by the reciprocal of \frac{6xy^{3}}{7x^{2}y^{2}}.

$$\frac{8x^{3}y^{4}\times 7x^{2}y^{2}}{14x^{2}y\times 6xy^{3}}$$

Cancel out 2\times 2\times 7xyx^{2}y^{3} in both numerator and denominator.

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

Differentiate w.r.t. x

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