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Split the equation into two : one that you are going to integrate, and the other one you want to differentiate. then, apply formula uv - integral(v * du)

As you can see from the question there are 6 parts that 270 needs to be divided by. One sixth of 270 is equal to 45 and so one of the parts is equal to 45. To get the ratio, you have to simply multiply th...

Finding normals and tangents to curves is a very common question in A-level maths papers, especially core 3 modules, giving between 5-8 marks depending on complexity. In order to start this question, the ...

Firstly, lets name each equation A and B- this will help us later. If I told you what x was, you would be able to use either equation to find y- easy! so lets first find one unknown (x or y) then use that...

This problem requires using the quotient rule, product rule and the chain rule. The derivative of the entire thing is ((du/dx)v-(dv/dx)u)/v^2 where u=2x+xe^6x and v=9x-2x^2-lnx. dv/dx is relatively strait...