Solve 10xy/12divx/20y^2*24x^4/60y^4

$$\frac { 10 x y } { 12 } \div \frac { x } { 20 y ^ { 2 } } \cdot \frac { 24 x ^ { 4 } } { 60 y ^ { 4 } }$$

Evaluate

$$\frac{20x^{4}}{3y}$$

Solution Steps

Divide \frac{10xy}{12} by \frac{x}{20y^{2}} by multiplying \frac{10xy}{12} by the reciprocal of \frac{x}{20y^{2}}.

$$\frac{10xy\times 20y^{2}}{12x}\times \frac{24x^{4}}{60y^{4}}$$

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

$$\frac{5\times 10yy^{2}}{3}\times \frac{24x^{4}}{60y^{4}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{5\times 10y^{3}}{3}\times \frac{24x^{4}}{60y^{4}}$$

Multiply 5 and 10 to get 50.

$$\frac{50y^{3}}{3}\times \frac{24x^{4}}{60y^{4}}$$

Cancel out 12 in both numerator and denominator.

$$\frac{50y^{3}}{3}\times \frac{2x^{4}}{5y^{4}}$$

Multiply \frac{50y^{3}}{3} times \frac{2x^{4}}{5y^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{50y^{3}\times 2x^{4}}{3\times 5y^{4}}$$

Cancel out 5y^{3} in both numerator and denominator.

$$\frac{2\times 10x^{4}}{3y}$$

Multiply 2 and 10 to get 20.

$$\frac{20x^{4}}{3y}$$

Differentiate w.r.t. x

$$\frac{80x^{3}}{3y}$$