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In order to get from f(x) to f''(x) we need to differentiate the function f(x) with respect to x and then differentiate the resulting function with respect to x again. When differentiating f(x), split the...

First of all remember to never be intimidated by a question. Don't read a question and say "I don't know," start with what you do know. In this case we know that every year the £12,00 initial va...

Full Question: A particle A of mass 2.5kg is at rest on a smooth inclined plane at an angle of 25 degrees, it is connected to a particle B of mass 1.5kg by a light inextensible string which lies along a l...

a) tan(A+B)=(tanA+tanB)/(1-tanAtanB) So, tan(2x)=[tan(x)+tan(x)]/[1-(tanx)(tanx)]. Therefore, tan(2x)=[2tan(x)]/[1-tan^2(x)] = 2p/(1-p^2). b) cos(x)=1/sec(x). Using other trigonometric identities, we know...

These are two really useful rules for differentiating functions. We use the chain rule when differentiating a 'function of a function', like f(g(x)) in general. We use the product rule when differentiatin...