Answer
a. $3$ times $y$
b. $3$ times $y$
c. $3$ times $y$
d. $2$ times $x$
Work Step by Step
a) In 3 times differentiating with respect to $y$ would have all vanished. Let's say we first differentiate with respect to $x$, than the term with e^{x} will remain till end which would make problem more complex
b) In 3 times differentiating with respect to $y$ would have all vanished. In case of $x$ the trigonometric function never ends so we don't go for variables with trigonometric function.
c) There is only 1 term with $y$ so the rest would become zero in the first derivation with respect to $y$, reducing the problem.
d) In 2 derivations with respect to $x$ everything would become zero. And $y$ is included in exponential so we don't derivate particular variables first in such cases.
