Solve a+x/sqrt[3]{a^2-sqrt[3]{x^2}}{sqrt[3]{a}-sqrt[3]{a}-sqrt[3]{ax}}-sqrt[3]{ax}+sqrt[3]{x^2}-sqrt[6]{x}

$$\frac { a + x } { \sqrt[ 3 ] { a ^ { 2 } } - \sqrt[ 3 ] { x ^ { 2 } } } { \sqrt[ 3 ] { a } - \sqrt[ 3 ] { a } - \sqrt[ 3 ] { a x } } - \sqrt[ 3 ] { a x } + \sqrt[ 3 ] { x ^ { 2 } } - \sqrt[ 6 ] { x }$$

Evaluate

$$\frac{\sqrt[6]{x}\left(\sqrt{x}a^{\frac{2}{3}}-\sqrt[3]{a}x^{\frac{5}{6}}-\sqrt[6]{x}a-\sqrt[6]{x}a^{\frac{2}{3}}-x^{\frac{5}{6}}+2\sqrt[3]{a}\sqrt{x}+\sqrt[3]{x}-\sqrt[3]{a}\right)}{\sqrt[3]{a}-\sqrt[3]{x}}$$

Differentiate w.r.t. x

$$\frac{4\sqrt[3]{a}x^{\frac{7}{6}}-2\sqrt[6]{x}a^{\frac{4}{3}}-8a^{\frac{2}{3}}x^{\frac{5}{6}}+4\sqrt{x}a-10\sqrt[3]{a}x^{\frac{5}{6}}-2\sqrt[6]{x}a+4x^{\frac{7}{6}}+8\sqrt{x}a^{\frac{2}{3}}+2\sqrt[3]{ax}-a^{\frac{2}{3}}-x^{\frac{2}{3}}}{6\left(\sqrt[3]{a}-\sqrt[3]{x}\right)^{2}x^{\frac{5}{6}}}$$