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First we have to use the product rule, remember that if we have h(x)=f(x)g(x) then h'(x)=f'(x)g(x)+f(x)g'(x).So h'(x) = x^3D[(x+1)^5]+(x+1)^5D[x^3]Completing the unfinished derivatives,h'(x) = x^3[5(x+1)^...

Sorry but it's a little hard to write the question out! I have the working on paper but I can't upload it. Ok so first you need to multiply out the brackets to make it a little easeier to look at and obta...

First step I would take would make it look less intimidating by converting all components into sin and cos i.e

2(((sinx)/(cosx))^2) + 1/((cosx)^2) = 1

Notice that there is a...

Log rules:

log(a) + log(b) = log(ab)

so, in this case, we must find x such that 7x = 21

thus x = 3

similarly, log(a) - log(b) = lo...

Note that sqrt(ab)=sqrt(a)sqrt(b)

Thus to have A, an integer, we must find the highest number 'a' that is a square number and is also a factor of 50.

So, a=25 and b=2 (ab=25...