⚠ 2x is read as the product 2*x: for a power, write 2^x‖(\partial)/(\partial x)(2x^2y+sin(x^3)) is read as dif(2x^2y+sin(x^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 differentiate: $\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}y+\sin \left(x^3\right))$

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

We differentiate using: $\frac{\mathrm{d}}{\mathrm{d}x}\left(\sin \left(f\right)\right)=\frac{\mathrm{d}}{\mathrm{d}x}\left(f\right)·\cos \left(f\right)$ (where f = $x^3$)

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

ℹ$\frac{\mathrm{d}}{\mathrm{d}x}\left(x^2\right)$ = $2x$‖$\frac{\mathrm{d}}{\mathrm{d}x}\left(x^3\right)$ = $3x^2$

$2y·2x+3x^2·\cos \left(x^3\right)$

$4yx+3x^2·\cos \left(x^3\right)$

$3x^2·\cos \left(x^3\right)+4xy$

▶Derivative:  $x·(3x·\cos \left(x^3\right)+4y)$