Search over 10,000 free study notes

(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) =...

so step 1) remove the denominator by multiplying (4-a) by p. Therefore obtaining p(4-a) = 3a+5. step 2) multiply out to get 4p-ap = 3a+5 step 3) have all the a's on one side, and non a's on other side. th...

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...