Solve 21y^12x^3/7y^54x^6/5{y^6{x}^6}

$$\frac{ 21 { y }^{ 12 } { x }^{ 3 } }{ 7 { y }^{ 5 } } \frac{ 4 { x }^{ 6 } }{ 5 { y }^{ 6 } { x }^{ 6 } }$$

Evaluate

$$\frac{12yx^{3}}{5}$$

Solution Steps

Cancel out 7y^{5} in both numerator and denominator.

$$3x^{3}y^{7}\times \frac{4x^{6}}{5y^{6}x^{6}}$$

Cancel out x^{6} in both numerator and denominator.

$$3x^{3}y^{7}\times \frac{4}{5y^{6}}$$

Express 3\times \frac{4}{5y^{6}} as a single fraction.

$$\frac{3\times 4}{5y^{6}}x^{3}y^{7}$$

Multiply 3 and 4 to get 12.

$$\frac{12}{5y^{6}}x^{3}y^{7}$$

Express \frac{12}{5y^{6}}x^{3} as a single fraction.

$$\frac{12x^{3}}{5y^{6}}y^{7}$$

Express \frac{12x^{3}}{5y^{6}}y^{7} as a single fraction.

$$\frac{12x^{3}y^{7}}{5y^{6}}$$

Cancel out y^{6} in both numerator and denominator.

$$\frac{12yx^{3}}{5}$$

Differentiate w.r.t. x

$$\frac{36yx^{2}}{5}$$