Solve frac{8x^{3}y^{5}}{16y^7}+8x^3y^5/16y^7=

$$\frac { 8 x ^ { 3 } y ^ { 5 } } { 16 y ^ { 7 } } + \frac { 8 x ^ { 3 } y ^ { 5 } } { 16 y ^ { 7 } } =$$

Evaluate

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

Solution Steps

Cancel out 8y^{5} in both numerator and denominator.

$$\frac{x^{3}}{2y^{2}}+\frac{8x^{3}y^{5}}{16y^{7}}$$

Cancel out 8y^{5} in both numerator and denominator.

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

Combine \frac{x^{3}}{2y^{2}} and \frac{x^{3}}{2y^{2}} to get 2\times \frac{x^{3}}{2y^{2}}.

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

Express 2\times \frac{x^{3}}{2y^{2}} as a single fraction.

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

Cancel out 2 in both numerator and denominator.

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

Differentiate w.r.t. x

$$3\times \left(\frac{x}{y}\right)^{2}$$