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The first thing to note about this question is that it's a simultaneous equations question, involving a quadratic. We will have to use substution in order to solve it. So first of all we need to chose whi...

When you differenciate a function, the constant term turns to 0. So a lot of different functions like x² + 7 and x² - 3 will have the same derivative, this means that going from the ...

The key to this question is to stay calm and not let yourself be intimidated. You can use the information provided in the question to give you a clear direction to head in- you want to factorise out root ...

1. When integrating remember the general rule: x^n --> x^(n+1)/(n+1). Now look at each term separately. 3x^(1/2) --> 3x^(3/2)/(3/2) = 2x^(3/2)-6x --> -6x^(2)/2 = -3x^24 = 4x^(0) --> 4x^(1)/...

Move y terms to the left hand side and the keep the x terms on the right hand side: dy*(1/(exp(4y))) = dx*(3x/(7+2x^(2))^(2))
First, solve the right hand side by using a substition: u = 7 + 2x^(...