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Using quotient rule y = u/v - dy/dx = (v.du/dx - u.dv/dx)/v².u = cos(2x³) , a = 2x³. du/da = -sin(a), da/dx = 6x². From chain rule, we know that du/dx = du/da ....

This question requires the use of differentiation by product rule. First differentiate the first term, whilst keeping the second term the same, i.e. we get 2xln(3x). Secondly we keep the first term the sa...

I would first always label the two equations as equation 1 equation 2. I would then look to see if you can cancel one of the variables out by adding or subtracting the two equations together. If this is p...

Firstly, for the points of intersection we need to equate the two expressions for y. Since we know that they intersect at the origin, we can immediately cancel the x values and then solve the quadratic fo...

Remember completing the square gives a result of the form (x+q)² + p where q and p are numbers
Also q is always half of the x term, which in this case is -4, as such q = -2
Substituti...