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With differentitaion you multiply the fatcor it's raised by and minus one from the order

e.g. y = x^n so y' = nx^(n-1)

So f'(x) = 3x^2 + 6x and f''(x) = 6x + 6

Teh points of intersection can be found by subbing in y=2x-1 to the equation of the circle. (x-5)²+(2x-1-3)²=5x²-26x+33=9 so we have 5x²-26x+24=0. Solving the q...

The product rule is used when two functions of x are multiplied by each other, hence, product. So this can be used to differnetiatate 3x²* x+1 or more complex functions like sinxcosx.

Th...

For the first part it would be a good idea to sketch out the graph. Then using the formula 'change in y/change in x' find the gradient of the line (-4/3). You can then either use the formula y=mx+c and pu...

To integrate ln(x) we will have to use integration by parts. 

The equation for integration by parts is: (then equation written on the whiteboard).

In the case of ln(x), let v=ln(x) ...