⚠ (\partial)/(\partial x)(cos(xln(y))) is read as (\partial)/(\partial x)(cos(x*ln(y))): use * for multiplication, use ^ for a power

⚠ (\partial)/(\partial x)(cos(x*ln(y))) is read as dif(cos(x*ln(y)),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: $\frac{\mathrm{d}}{\mathrm{d}x}\left(\cos (x·\ln \left(y\right))\right)$

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

$-\frac{\mathrm{d}}{\mathrm{d}x}(x·\ln \left(y\right))·\sin (x·\ln \left(y\right))$

▶Derivative:   $-\ln \left(y\right)·\sin (x·\ln \left(y\right))$