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Write y = x^xln(y) = xln(x)1/y dy/dx = (1+ln(x)) by applying the chain rule to the LHS and product rule to the RHSdy/dx = y(1+ln(x)) Rearranging dy/dx = x^x (1+ln(x)) Substituting y=x^x into the equationN...

The easiest way to do this is to notice that f(x-2) is just f(x) translated by two in the positive x-direction - it is not necessary to calculate what f(x-2) is at any point!
So we calculate f'(x) =...

Recall the product rule for differentiation: the derivative of uv is equal to u'v+uv'.If we use the fact that integration reverses differentiation (so the integral of f' is f), then we calculate that uv i...

Pressure groups have been very influential in the USA because they are able to shape debate, shape agenda and determine outcomes. However others have argued that party and voters have more influence...

Key idea - total angular momentum of the system is conserved. Before the collision: angular momentum of earth is given by L_E=Iw_E, here w_E is the angular velocity of Ea...