Search over 10,000 free study notes

As this is a product of two functions it is necessary to use the product rule for differentiation. Therefore one of the functions must labeled v and the other u. i.e. u=x^3 and v=(x^2+1). It is then neces...

Please note that this solution is easier to explain with 2 diagrams 

The side opposite of the 30 degree angle: 

If we have the hypotenuse and require the length of the opposite side then we ...

Absolute poverty is characterised by acute deprivation of human needs such as: food, safe drinking water, shelter, education and information. Consequently, absolute poverty is seen mostly in low economica...

A chemical called a neurotransmitter passes from one neurone to the next causing an electrical impulse.

 y = ln(2x+3 / 7x^3 +1)

d/dx(2x+3 / 7x^3 + 1) by quotient rule which is(v.du/dx - u.dv/dx) / v^2  where u=2x+3 and v=7x^3 +1   gives (-27x^3 -63x^2 +2) / (7x^3 +1)^2

so d/dx(ln(2x+3 / 7x^3 +...