Solve (frac{lambda^{4}z^{2}}{4y^5})(2x^3y^2/7^3)

$$( \frac { \lambda ^ { 4 } z ^ { 2 } } { 4 y ^ { 5 } } ) ( \frac { 2 x ^ { 3 } y ^ { 2 } } { 7 ^ { 3 } } )$$

Evaluate

$$\frac{\left(\frac{x}{y}\right)^{3}z^{2}\lambda ^{4}}{686}$$

Solution Steps

Calculate 7 to the power of 3 and get 343.

$$\frac{\lambda ^{4}z^{2}}{4y^{5}}\times \frac{2x^{3}y^{2}}{343}$$

Multiply \frac{\lambda ^{4}z^{2}}{4y^{5}} times \frac{2x^{3}y^{2}}{343} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\lambda ^{4}z^{2}\times 2x^{3}y^{2}}{4y^{5}\times 343}$$

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

$$\frac{z^{2}x^{3}\lambda ^{4}}{2\times 343y^{3}}$$

Multiply 2 and 343 to get 686.

$$\frac{z^{2}x^{3}\lambda ^{4}}{686y^{3}}$$

Differentiate w.r.t. x

$$\frac{3\lambda ^{4}\left(xz\right)^{2}}{686y^{3}}$$