Solve 8x^2/3y^4*21y^2/16x^3

$$\frac { 8 x ^ { 2 } } { 3 y ^ { 4 } } \times \frac { 21 y ^ { 2 } } { 16 x ^ { 3 } }$$

Evaluate

$$\frac{7}{2xy^{2}}$$

Solution Steps

Multiply \frac{8x^{2}}{3y^{4}} times \frac{21y^{2}}{16x^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8x^{2}\times 21y^{2}}{3y^{4}\times 16x^{3}}$$

Cancel out 3\times 8x^{2}y^{2} in both numerator and denominator.

$$\frac{7}{2xy^{2}}$$

Differentiate w.r.t. x

$$-\frac{7}{2\left(xy\right)^{2}}$$