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This type of question appears over-complicated with limited options, but one must not fear! At first, the numerator seems to be of a higher degree than the denominator (x^4 compared to x^2), but from the ...

Using the product rule, f=uv, df = (vu'-uv')/v^2. we first set u = 3x^2 and v = sin(2x). u' = 6x, v'=2cos(2x) Therefore, vu' = 6xsin(2x). uv' = 6x^2cos(2x), v^2 = 4cos^2(2x) Therefore the differe...

If there is an increase in saving, then assuming that income stays exactly the same, this will mean that there is a fall in spending as we are saving a higher proportion of our income - or in other words ...

To answer this question, we need to make y the subject of the second equation. We can do this through simple rearrangement:

y-3x=13 so y=13+3x

Now that we have y on its own, this means we ca...

Use the product rule: u'v + uv' u = 2x     V= sin3x u'= 2       v'= 3cos3x = (2)(sin3x) + (2x)(3cos3x) = 2sin3x + 6xcos3x