Solve frac{6sqrt[x-y]{9y}+sqrt[x-y]{9x}}{x-sqrt[y]{3^x+y}}

$$\frac{ 6 \sqrt[ x-y ]{ 9y } + \sqrt[ x-y ]{ 9x } }{ x- \sqrt[ y ]{ { 3 }^{ x } +y } }$$

Evaluate

$$\frac{6\times \left(9y\right)^{\frac{1}{x-y}}+\left(9x\right)^{\frac{1}{x-y}}}{-\left(y+3^{x}\right)^{\frac{1}{y}}+x}$$

Differentiate w.r.t. x

$$\frac{xy\ln(x)\times \left(9x\right)^{\frac{1}{x-y}}\left(y+3^{x}\right)^{\frac{1}{y}}+y^{2}\times \left(9x\right)^{\frac{1}{x-y}}\left(y+3^{x}\right)^{\frac{1}{y}}+6xy\ln(y)\times \left(9y\right)^{\frac{1}{x-y}}\left(y+3^{x}\right)^{\frac{1}{y}}-xy\times \left(9x\right)^{\frac{1}{x-y}}\left(y+3^{x}\right)^{\frac{1}{y}}+6\ln(3)xy^{2}\times 3^{x}\left(y+3^{x}\right)^{\frac{1-y}{y}}\times \left(9y\right)^{\frac{1}{x-y}}+\ln(3)xy^{2}\times 3^{x}\left(y+3^{x}\right)^{\frac{1-y}{y}}\times \left(9x\right)^{\frac{1}{x-y}}-2\ln(3)yx^{2}\times 3^{x}\left(y+3^{x}\right)^{\frac{1-y}{y}}\times \left(9x\right)^{\frac{1}{x-y}}-12\ln(3)yx^{2}\times 3^{x}\left(y+3^{x}\right)^{\frac{1-y}{y}}\times \left(9y\right)^{\frac{1}{x-y}}+6\ln(3)x^{3}\times 3^{x}\left(y+3^{x}\right)^{\frac{1-y}{y}}\times \left(9y\right)^{\frac{1}{x-y}}+\ln(3)x^{3}\times 3^{x}\left(y+3^{x}\right)^{\frac{1-y}{y}}\times \left(9x\right)^{\frac{1}{x-y}}+2\ln(3)xy\times \left(9x\right)^{\frac{1}{x-y}}\left(y+3^{x}\right)^{\frac{1}{y}}+12\ln(3)xy\times \left(9y\right)^{\frac{1}{x-y}}\left(y+3^{x}\right)^{\frac{1}{y}}+2\left(xy\right)^{2}\times \left(9x\right)^{\frac{1}{x-y}}+12\left(xy\right)^{2}\times \left(9y\right)^{\frac{1}{x-y}}-yx^{2}\ln(x)\times \left(9x\right)^{\frac{1}{x-y}}-xy^{3}\times \left(9x\right)^{\frac{1}{x-y}}-yx^{3}\times \left(9x\right)^{\frac{1}{x-y}}-6yx^{2}\ln(y)\times \left(9y\right)^{\frac{1}{x-y}}+yx^{2}\times \left(9x\right)^{\frac{1}{x-y}}-6xy^{3}\times \left(9y\right)^{\frac{1}{x-y}}-6yx^{3}\times \left(9y\right)^{\frac{1}{x-y}}-xy^{2}\times \left(9x\right)^{\frac{1}{x-y}}-2\ln(3)yx^{2}\times \left(9x\right)^{\frac{1}{x-y}}-12\ln(3)yx^{2}\times \left(9y\right)^{\frac{1}{x-y}}}{xy\left(\left(x-y\right)\left(-\left(y+3^{x}\right)^{\frac{1}{y}}+x\right)\right)^{2}}$$