Search over 10,000 free study notes

To start off with, we have the expression y = x^x and we want to differentiate it. A clever way to do this would be to first remember implicit differentiation and start by taking the natural logarithm of ...

The question is pretty straightforward and asks you to find the derivative of y, which is a function of x. The most simple way to do this is to first eliminate the brackets and then derive. Thus we get y=...

The turning point of a curve is the point at which it will turn, therefore, either the maximum or minimum point. Firstly, you need to expand out the brackets so the equation looks like a standard curve eq...

One good way is to use the formula y - y₁ = m(x - x₁)where (x₁,y₁) is a point on the line and m is the gradient of the line. This is derived from the definitio...

The equation for a line is y(x)=ax+b.Because it intersects the y axis at x=0 at y=1y(x)=b=1a is equal to the gradient of the function so the line is given as y(x)=3x+1In order to get the two intersection...