Question: Evaluate the following:

a) \[\frac{dy}{dx}\] if y= \[\frac{x}{\sin x}\]

b) f “(x) if f(x)=x⁵+3x²-6

c) \[\frac{dy}{dx}\] if x²y³+y³=4

d) the rate of change of f(x)=e^sinx at x=0

e) \[\int\limits_{1}^{2}{\frac{1}{x}dx}\]

f) \[\int{({{x}^{3}}-6x+5})dx\]