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The chain rule is used when we have a function in the form f(g(x)).

For example sin(x^3). [In this case, f(x) = sin(x) and g(x) = x^3]

The chain rule says that the derivativ...

'Factorise' essentially means put into a simpler form, in this case with two sets of linear equations which would multiply out to give the quadratic equation shown above.

What we are look...

The question can be broken into two steps, 

1) dy/dx is asking to differentiate y=x³+5x+3 with respect to x

Differentiating we multiply by the current power and l...

When you differentiate, you multiply by the old power and decrease the power by 1. If the expression has a constant in it, this differentiates to 0. 

So the answer is 3y^(3-1) + ...

You want two numbers that multiply to give 2 and add to give 3. Looking at factors is always easiest, so start by listing pairs of numbers that multiply together to give 2. There are ...