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This answer is easiest explained using the whiteboard in the interview. The question is basically asking for algebraic long division, we know (x+3) is a factor and are tasked with finding the other 2. We ...

(Much easier to explain in conversation and with drawings): But, 

An application of the quotient rule, stating that for f(x)=a(x)/b(x), f'(x) = a'(x)b(x) - a(x)b'(x) all over [b(x))]^2 Here, a(x) =...

Use the product rule: Let   u = cos3x ,     v = cosec4x Then du/dx = -3sin3x , dv/dx = -4cosec4xcot4x  (standard result, given in the formula booklet) Hence dy/dx = -4cosec4xcot4xcos3x - 3sin3xcosec4x . (...

• Think about which process we need to determine the turning point? - Differentiation 

• Think about the form of the given function. - Product of two functions, so use Product Rule...

When you are asked to integrate a function f(x), you are really being asked the question: "what function F(x) exists such that when you take its derivative, you are left with f(x)?"

Let u...