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Integration by parts is used when you would like to find the integral of a composite function made up of two functions of the same variable as which you're integrating with respect to. 

T...

Skew lines in 3 dimensions are those which are not parallel and do not intersect.

Let's take two example lines: l₁ = (2, 2, -1) + λ(3, 1, -3) and l₂ = (1, 0, 1) + µ(...

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)<...