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Firstly, we need to differentiate the equation to find an equation for the gradient of the line.dy/dx = 6x-12We know the original graph was quadratic, and therefore only has one stationary point. This is ...

3l²mn + nl²m - 5mn²l + l²nm + 2n²ml - mn²
The first step is to ask yourself if there is anything that could help you simplify the equ...

∫  Cosec (x)/Sec (x) dx∫  [1/Sin (x)]/ [1/Cos (x)] dx∫  [1/Sin (x)] * [Cos (x)] dx∫  Cot (x)= ln [Sin (x)] + c

We can write the two numbers as x and 1000-x, because x+(1000-x) = 1000 for any x we pick. Now we want to maximise the product x(1000-x); expanding the brackets gives us 1000x-x² which is easie...

Using the chain rule we differentiate the ‘outside function’, then differentiate the ‘inside function’ and multiply both derivatives together giving 2sin(x)cos(x)