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Use the product rule d(u.v)/dx = u.(dv/dx) + v(du/dx). Calculate the LHS as such first. (Demonstrate on whiteboard.) Then calculate the RHS. (Demonstrate on whiteboard.) Group the dy/dx terms on one side ...

Using the fact that 1/3rd of the fruit in bag 1 are apples and there are 20 apples in total you can work out that there are 60 pieces of fruit in bag 1. This is found by doing 20 x 3 = 60.

Then usi...

2(e-2f) + x(e-2f) = (2+x)(e-2f)

When we find dy/dx we find the gradient of the curve at (3,1). Start by differentiating the left hand side (LHS) like so.. (whiteboard). Remember every time we differentiate a y value we multiply by dy/dx...

This equation rearranges to give -y=(x+3)^2-4, which is very similar to our curve y=(x+3)^2-4 from before. In fact, replacing y with -y in an equation is equivalent to reflecting the curve through the x-a...