What trig subsitution is

Trig substitution is a fancy kind of substitution used to help find the integral of a particular family of fancy functions. These fancy functions involve things like a2 + x2 or a2 – x2 or x2 – a2 , usually under root signs or inside half-powers, and the purpose of trig substitution […]

It seems like ages ago — but it was only yesterday — that I wrote about differentiating functions with the variable in both the base and the power. Back there, I had learned that the derivative of a function like f(x)g(x) is the sum of the derivative when you pretend f(x) is constant and the […]

In Maths 1A here at the University of Adelaide, they learn the following theorem (this is taken from the lecture notes written by the School of Maths here):

It says that, given a function of x defined as the integral of an original function from a constant to x, when you differentiate it you get the […]

I was talking to a student about his calculus last week. He was trying to differentiate xx. (Actually he was trying to differentiate x ln(x) and had decided the best place to start was to raise e to the power of it, thus producing xx.) At first he tried this:

I asked him what he thought […]