⚠ (\partial)/(\partial x)(x^{2/3}+y^{2/3}) is read as dif(x^(2/3)+y^(2/3),x): use dif(expression, variable) for a derivative with respect to that variable, use (numerator)/(denominator) for a quotient, use ^(...) to group an exponent, use * to multiply

Differentiate with respect to x while holding y constant

Let's perform the differentiation: $\frac{\mathrm{\partial }}{\mathrm{\partial }x}(x^{\frac{2}{3}}+y^{\frac{2}{3}})$

ⓘ The derivative of a sum is the sum of the derivatives: $\frac{\mathrm{\partial }}{\mathrm{\partial }x}(x^{\frac{2}{3}}+y^{\frac{2}{3}})$ = $\frac{\mathrm{\partial }}{\mathrm{\partial }x}\left(x^{\frac{2}{3}}\right)+\frac{\mathrm{\partial }}{\mathrm{\partial }x}\left(y^{\frac{2}{3}}\right)$

$\frac{\mathrm{\partial }}{\mathrm{\partial }x}\left(x^{\frac{2}{3}}\right)+\frac{\mathrm{\partial }}{\mathrm{\partial }x}\left(y^{\frac{2}{3}}\right)$

ⓘ The derivative of x^n is n*x^(n-1): $\frac{\mathrm{\partial }}{\mathrm{\partial }x}\left(x^{\frac{2}{3}}\right)$ = $\frac{2}{3}·x^{-\frac{1}{3}}$■The derivative of a constant is zero: $\frac{\mathrm{\partial }}{\mathrm{\partial }x}\left(y^{\frac{2}{3}}\right)$ = $0$

$\frac{2}{3}·x^{-\frac{1}{3}}+0$

ⓘ Adding 0 changes nothing: $\frac{2}{3}·x^{-\frac{1}{3}}+0$ = $\frac{2}{3}·x^{-\frac{1}{3}}$■Multiplying a fraction by a term multiplies its numerator: $\frac{2}{3}·x^{-\frac{1}{3}}$ = $\frac{2x^{-\frac{1}{3}}}{3}$■The factor is moved to the numerator or the denominator by changing the sign of its exponent, for a nonzero base: $\frac{2x^{-\frac{1}{3}}}{3}$ = $\frac{2}{3x^{\frac{1}{3}}}$

▶Derivative:   $\frac{2}{3x^{\frac{1}{3}}}$