Solve 3xy^4/2x^5y6x^2y^2/4{y^}

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

Evaluate

$$\frac{9y^{4}}{4x^{2}}$$

Solution Steps

Cancel out xy in both numerator and denominator.

$$\frac{3y^{3}}{2x^{4}}\times \frac{6x^{2}y^{2}}{4y^{1}}$$

Cancel out 2y in both numerator and denominator.

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

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

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

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

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

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

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

Multiply 3 and 3 to get 9.

$$\frac{9y^{4}}{2\times 2x^{2}}$$

Multiply 2 and 2 to get 4.

$$\frac{9y^{4}}{4x^{2}}$$

Differentiate w.r.t. x

$$-\frac{9y^{4}}{2x^{3}}$$