Differentiation of Trigonometric Functions: Exercise 1

00:01 So I hope you had fun attempting some of the less challenging and the more challenging questions in the exercise.

00:06 Remember that you are using a vast amount of knowledge now, so not just differentiation simply.

00:12 You're using chain rule, product rule, quotient rule.

00:15 You're using all the new facts that we've learned by differentiating sin, cos, and tan and different identities. But anyway, let's just check that you've done it correctly and we'll go through the answers together now.

00:27 So, the first question asked you to differentiate y equals to cos x to the power of 15.

00:33 So we're looking at y equals to cos x to the power of 15.

00:39 Now the reason I've rewritten this question is so that we can see firstly what kind of question this is. Remember what I said, the first thing that you need to do is just take a moment to look at your question and to observe what nature the question is.

00:54 So you have cos x to the power of 15, all to the power of 15.

00:59 You can see that the way that it's written here is trying to help you identify that this is a big function and then you have a little function.

01:06 So you have something to the power of 15, and then inside, you have a different function.

01:12 So let's just start with differentiating the brackets to the power of 15.

01:17 You simply bring the power down, leave whatever is inside, and decrease the power by 1.

01:24 You then multiply it with the differential of the inside.

01:28 So you now need to recall what is the differential of cos x and the differential of cos x is minus sin x and then you put it together.

01:37 So 15 times minus sin x will just give you minus 15 sin x and then that is still multiplying with cos x to the power of 14.