Math Shorts - Derivatives by Bektas Metin

Author:Bektas, Metin [Bektas, Metin]
Language: eng
Format: epub
Published: 2014-08-29T16:00:00+00:00

(Plot of the tangent function)

Time to differentiate! The derivative of the sine function is:

So we "duplicate" the factor b outside the bracket and change sine to cosine. The derivative is also periodic, which makes sense. Since the graph of the sine function goes up and down periodically, the same should be true for its slope. On to the cosine function:

We "duplicate" the factor b outside the bracket, change cosine to sine and change the sign of the function. Note that this implies that when differentiating sine and cosine functions, we're stuck in a loop when it comes to higher-order derivatives. We start with sine, this changes to cosine in the first derivative, which changes back to (minus) sine in the second derivative, which becomes (minus) cosine in the third derivative, which turns into sine in the fourth derivative and then it all repeats.

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