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The area under a curve is analytically calculated using the integral of the function. The integral of the function above could be calculated using integration by parts twice, considering that 3 functions ...

Sure. If you remember how to calculate d/dx(uv) then you can understand how integration by parts works. d/dx(uv) = u(dv/dx) + v(du/dx). we can re-arrange this: u(dv/dx) = d/dx(uv) - v(du/dx). Now integrat...

First we have to identify that implicit differentiation is used to solve this question. We can differentiate the first the LHS first, by using the chain rule, we know that the differentiation of e^(xy) is...

Since L is parallel to y=4x+5 we know that the two lines have the same gradient. The gradient of a line in the form y=ax+b has is a, which means the gradient of y=4x+5 is 4, so L is y=4x+b and we just nee...

A function of the form shown in the question is called a composite function, it is a 'function of a function'. It can be differentiated by expanding the brackets and differentiating each term individually...