Solve x(2y%)(2y%)

$$x(2y \% )(2y \% )$$

Evaluate

$$\frac{xy^{2}}{2500}$$

Solution Steps

Multiply \frac{y}{100} and \frac{y}{100} to get \left(\frac{y}{100}\right)^{2}.

$$x\times 2\times \left(\frac{y}{100}\right)^{2}\times 2$$

To raise \frac{y}{100} to a power, raise both numerator and denominator to the power and then divide.

$$x\times 2\times \frac{y^{2}}{100^{2}}\times 2$$

Multiply 2 and 2 to get 4.

$$x\times 4\times \frac{y^{2}}{100^{2}}$$

Calculate 100 to the power of 2 and get 10000.

$$x\times 4\times \frac{y^{2}}{10000}$$

Express x\times \frac{y^{2}}{10000} as a single fraction.

$$\frac{xy^{2}}{10000}\times 4$$

Cancel out 10000, the greatest common factor in 4 and 10000.

$$\frac{xy^{2}}{2500}$$

Differentiate w.r.t. x

$$\frac{y^{2}}{2500}$$