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Firstly, what are we trying to achieve by differentiating a function? Differentiation allows us to compute the rate of change of a function at any point along a well behaved function. Consider the curve y = ...

The chain rule is most commonly seen in Leibniz's notation, which is as follows:<o:p></o:p> dz/dx = dz/dy * dy/dx<o:p></o:p> You can remember it intuitively by thinking of the two 'dy...

The maximum/minimum of a function are the points where the first derivative (the gradient) of the function is zero. So with a function of the form y=f(x), you must take the derivative (dy/dx) and set your re...

If we have the 2 lines line 1 - 3y=4x+2 and line 2 - 6y=7x+3 Firstly we would look for when the y's or x's are multiples of each other in this case the y's are multiples of each other as 3 is a multiple of 6...

From the double angle formula for cosine, we know that cos(2x)=cos 2 (x)-sin 2 (x). Also, we know that sin 2 (x)+cos 2 (x)=1. So by substituting the second formula into the first, we can say that cos(2x)=(1-...