Differentiation of Trigonometric Functions: Examples

by Batool Akmal

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    So, let?s actually start doing some numerical examples using sin, cos, and tan. Let?s look at our first example here which asks you a nice straightforward question and it?s asking us to differentiate y equals to 3 tan x. All we need to remember is what does tan differentiate to. So you can look it up in your notes to start with but eventually, we should be able to know these by heart so we can at least differentiate sin, cos, and tan, without having to look them up or derive them. So we have our function y equals to 3 tan of x. It?s no different from general differentiation. You just have to differentiate and you have to differentiate this but this time we use the rules, so we know what tan differentiates to. So when we differentiate this, dy/dx, the 3 is just a constant so that can stay there, and then you have tan x which we want to differentiate and remember that tan differentiates to sec squared of x as we?ve just arrived or we?ve seen in the rules at the start, and that?s simply the answer. So there?s nothing more to it, all we?re doing is changing these trig functions to their standard differentials, if you?ll know them, it just takes less than 5 seconds to differentiate something as simple as 3 tan x to 3 sec squared x. So let?s build this up now. We now look at our second example where we?re now dealing with a cos function but there?s something a little bit more interesting about this so let?s just write this out. We have y equals to 5 cos of 3x, notice now that this is a cos function, but it?s not just a cos function, it?s cos of a different...

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    The lecture Differentiation of Trigonometric Functions: Examples by Batool Akmal is from the course Differentiation of Trigonometric Functions.

    Author of lecture Differentiation of Trigonometric Functions: Examples

     Batool Akmal

    Batool Akmal

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