# TAG: calculus

#### Zooming in to see the slope

A lot of people introduce the derivative at a point as the slope of the tangent at that point, which to me is quite confusing. It seems to me that the reason we want the derivative is that it is a measure of the slope of our actual function at that point, not the slope […]

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#### How I choose which trig substitution to do

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 […]

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#### Holding the other parts constant: it’s everywhere!

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 […]

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#### Problem strings and using the chain rule with functions defined as integrals

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 […]

#### Differentiating exponents: two wrongs make a right

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 […]

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