Solve frac{3x^{5}y^{4}}{4x^{2}y^2}*8x^6y^3/12x^3y

$$\frac { 3 x ^ { 5 } y ^ { 4 } } { 4 x ^ { 2 } y ^ { 2 } } \times \frac { 8 x ^ { 6 } y ^ { 3 } } { 12 x ^ { 3 } y }$$

Evaluate

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

Solution Steps

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

$$\frac{3y^{2}x^{3}}{4}\times \frac{8x^{6}y^{3}}{12x^{3}y}$$

Cancel out 4yx^{3} in both numerator and denominator.

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

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

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

Cancel out 2\times 3 in both numerator and denominator.

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

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{y^{4}x^{3}x^{3}}{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

Differentiate w.r.t. x

$$3y^{4}x^{5}$$