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First we can equate (19x - 2)/((5 - x)(1 + 6x)) to A/(5-x) + B/(1+6x) which means:
(19x - 2)/((5 - x)(1 + 6x)) = A/(5-x) + B/(1+6x). Then we will turn the RHS into a single fraction:

(19x - 2...

We first want to get every term in terms of the same variable, namely sin(x). to do so, we will use the identity sin^2(x) +cos^2(x) = 1 to get: 4(1-sin^2(x)) -15sin(x) -13 = 0. which we can then rewrite a...

A neurones role is to transmit electrical impulses rapidly around the organisms body so that the organism can respond to changes in both their external and internal environments. Their structure consists ...

By taking the natural log on both sides we can see that: ln(f(x)) = ln(x)^2 This is a more familiar expression that we know how to differentiate  LHS: f '(x)/f(x), RHS: 2*ln(x)/x By re...

First differentiate y with respect to x, which gives you dy/dx = 8 - 2x^-2. This needs to equal zero so equate to zero. 8-2x^-2 = 0. You can then bring the 2x^-2 to the other side giving 2x^-2=8. Dividing...