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Firstly, we calculate the y-value when x=1, namely y=e. Then we need to find the gradient of this curve at x=1, which can be determined by taking the derivative of y and then valuate it at x=1. So dy/d...

There are two ways in which this we can do this,

The first is explanding the brackets to get 1+2x+x² and differentiating to get 2+2x.

The second way is using the ...

The product rule is used when finding the derivative of the product of two functions - two functions multipled together.

If y = f(x)g(x), then

dy/dx = f'(x)g(x) + f(x)g'(x)<...

At first, you might think that it is possible to perform this integral simply by inspection, using the 'backwards chain rule'. This method would consist of adding one to the power, to get cos³(...

The standard rule for integration is: integrate kx^n dx = kx^(n+1)/(n+1). However, if we try and integrate 1/x in this manner we get, x^0/0, i.e. 1/0, which is infinity. However, if we look at a graph of ...