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Looking at this question the first thing we should notice is that there is a an x squared inside a bracket which is also squared. As there is function inside a function we must use the chain rule. The simple...

Notice that integration is simply the opposite of differentiation. So, if we just integrate this term-by-term then we can find an expression of y in terms of x. So, when we integrate dy/dx becomes y. Integra...

Remember that the equation of a straight line (when given two points OR a point and a gradient) is y-y_1 = m(x-x_1) where m is the gradient and (x_1,y_1) is a point on the line. Since we have two points, we ...

Rates and differential equations is a topic many students find difficult, especially when solving the differential equation is combined with techniques from other topics on the C4 syllabus. I hope my walkthr...

Firstly we must notice that we can differentiate each term separately. Starting with the 2xy term, we must use the product rule as x and y are two variable that will differentiate. Setting u=2x and v=y and u...