Question 1032805
 *[illustration trig_D]. *[illustration derivative_ruless].
apply respective rules:
f(x) = {{{sqrt( x) cos (x) }}} |Apply Multiplication Rule
f' = {{{cos(x)/2sqrt(x) - sqrt(x)sin(x)}}}
g(x) = {{{(x^3 + 1)/sin (x) }}}  |Apply Division Rule
g' = {{{ (3x^2sinx - (x^3 + 1)cos(x))/sin^2(x))) or {{{{{{ (3x^2/sin(x) - (x^3 + 1)cos(x))/sin^2(x)))
h(x) = {{{e^x sin(2x) }}}   |Apply Multiplication Rule / chain rule
h' = {{{2(e^x) cos(2x) + (e^x) sin(2x)}}}  0r {{{(e^x)(sin(2x) + 2cos(2x))}}}
k(x) = {{{x^2 / log x}}}  |Apply Division Rule
k' = {{{ (2xln(x) - x^2(1/x))/ln^2(x) }}} or {{{2x/ln(x) - x/ln^2(x)}}}