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Okay so consider (2 + x)^-1, we can only do the expansion we know if the bracket starts with a 1, to fix this we can factor a 2 out of the bracket so that it becomes (2(1 + x/2))^-1. Then by our rules of ...

As this is not in the common form and is HomogeneousStudents should be confident to understand what differentiation does.Using the quotient rule as well as implicit differentiation we look at each part of...

First differentiate the equation: dy/dx = 6x^2 - 6xSet this equal to 0 as at turning points the change in gradient is 0: 0 = 6x^2 - 6x6x(x-1)=06x=0 therefore x=0(x-1)=0 therefore x=1x=1,0Now substitute ba...

The key to this problem is to apply sec to both sides, and then differentiate implicitly: sec(y)=x; dsec(y)/dx = 1; tan(y)sec(y)dy/dx = 1; dy/dx = 1/(tan(y)sec(y)). Then using the fact that sec(y)=x and t...

Drawing the graphs of the trigonometric functions sin, cos & tan, we can see that they all extend along the x-axis to infinity. Indeed, the sin & cos functions move between 1 and -1 on the y-axis,...