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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...

Let u=2a+3, therefore du/da=2. Let y=u^5/2, therefore dy/du=5/2(u)^3/2 Hence dy/da=du/da*dy/du=2(5/2)*u^3/2=5u^3/2

So for this question you would need to know the formula for the area of a circle. This is Area = πr^2. In this formula, r = the radius. We are given the radius in the question. So all we need to do is put...

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...