⚠ (\partial)/(\partial x)(x+y^3) is read as dif(x+y^3,x): use dif(expression, variable) for a derivative with respect to that variable, use (numerator)/(denominator) for a quotient

Differentiate with respect to x while holding y constant

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

ⓘ The derivative of a sum is the sum of the derivatives: $\frac{\mathrm{\partial }}{\mathrm{\partial }x}(x+y^3)$ = $1+\frac{\mathrm{\partial }}{\mathrm{\partial }x}\left(y^3\right)$

$1+\frac{\mathrm{\partial }}{\mathrm{\partial }x}\left(y^3\right)$

ⓘ The derivative of a constant is zero: $\frac{\mathrm{\partial }}{\mathrm{\partial }x}\left(y^3\right)$ = $0$

$1+0$

ⓘ Adding 0 changes nothing: $1+0$ = $1$

▶Derivative:   $1$