## Derivatives of 'Elementary' Trigonometric Functions

Here, we try to determine the derivative of the function y=sin(x).

one way of figuring it out would be doing the limit calculations on your own.The other way would be reading the next paragraph.

Countless many have done the calculations before you. the derivative of sin(x) is cos(x). The derivative of cos(x) is -sin(x).

now on your own, you should use the quotient rule and the power rule to obtain the derivatives for respectively, tan(x), sec(x), and csc(x).

After you finish, (Memorize them!)

A hint on tan(x):

tan'(x)=sec(x)^2

Now what is really messy is when the trigonometric function "builds up". That is, what if we encounter some function that is composed of a bunch of sins and cos's mixed up? What if something likes sin(x^2+7)^5 pops up? Things are going to clear up a bit, but still, sometimes, problems tend to remain tough.

This is when your trigonometric skills come in. And memorization follows.

There are really no better ways to calculate cos(2x) than

one way of figuring it out would be doing the limit calculations on your own.The other way would be reading the next paragraph.

Countless many have done the calculations before you. the derivative of sin(x) is cos(x). The derivative of cos(x) is -sin(x).

__(MEMORIZE IT!____)__now on your own, you should use the quotient rule and the power rule to obtain the derivatives for respectively, tan(x), sec(x), and csc(x).

After you finish, (Memorize them!)

A hint on tan(x):

tan'(x)=sec(x)^2

Now what is really messy is when the trigonometric function "builds up". That is, what if we encounter some function that is composed of a bunch of sins and cos's mixed up? What if something likes sin(x^2+7)^5 pops up? Things are going to clear up a bit, but still, sometimes, problems tend to remain tough.

This is when your trigonometric skills come in. And memorization follows.

There are really no better ways to calculate cos(2x) than

__remembering__it is 2cos(x)^2-1.(double angle identity) so, when you have the time, eat your way through a trigonometry book.