Search over 10,000 free study notes

Recall that the derivative of exp(x) is exp(x), but notice this question is slightly more complex due to the x^2 term. This is example of differentiationg composite functions, and so the chain rule is req...

We can understand this identity in two different, useful ways.

Firstly, we can use Euler's identities from trigonometry to obtain the desired result using straightforward algebra. We know that:

Consider the triangle ABC. Denote h the altitude through B and D the point where h intersects the (extended) base AC
Cosine function for triangle ADB.

cos α= x/c  =>  x=c*cos α
 

Using: Tan(x) = Sin(x)/Cos(x)

Using: Cos(x) = sqrt(1-Sin²(x))

Cos(A) = sqrt(1-Sin²(A)) = sqrt(1-1/3) = sqrt(2)/sqrt(3)

Therefore: Tan(A) = Sin(A)/Cos(A) = (1/sqr...

The "chain rule" is a handy little tool that we can use to find the derivative of a complicated function.  Specifically, we use the chain rule when we have functions within functions.  But what ...