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Differentiation Basics

by Batool Akmal
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    00:02 Welcome to calculus methods.

    00:04 Now previously we've looked extensively in differentiation from first principles.

    00:09 And we've also now observed a much faster way of differentiating.

    00:14 In this lecture, we are now going to take faster method and we are actually going to start looking at some application of differentiation.

    00:21 So, we're going to go over the differentiation basics today.

    00:28 We'll look at the standard method of differentiation which is the faster method that we've just spoken about.

    00:34 And we'll practice it with few more questions.

    00:37 And then we're going to move on to more exciting bits which are the applications of it.

    00:41 So we're going to look at gradients of a particular point on a curve.

    00:45 How to find equations of tangents.

    00:47 How to find equations of normals.

    00:49 And again this is really useful for courses like medicine where you are actually looking at gradients of curves.

    00:56 So that you can work out and the steepness or the speed, that things are growing or decaying with.

    01:03 So previously we have found the gradient of a function like this 3x(squared) + 5x-1 using the definition of first principles.

    01:12 We applied the really long formula and came to the final answer.

    01:16 Where we made the delta X or the limit of delta X go to 0.

    01:21 But thankfully to modern calculus we now have much faster ways of doing this.

    01:25 And we discuss that faster way previously where you bring the power down and multiply it, and you decrease the power by 1.

    01:32 Remember what we said that any constant at the end go to 0 or they just disappear.

    01:40 As a little recap we will have a look at the general rule once again.

    01:44 So if you have a function y = x to the power of n.

    01:49 You bring the power down as the multiple of X to the power of n as we do here.

    01:55 And then you decrease the power by 1.

    01:58 So the answer will then be nx to the n - 1.

    02:02 Remember we've discussed this before just by observation, looking at differentiation from first principles.

    02:08 Also we've done some questions on this.

    02:11 And we've also derived it and proved to ourselves that this is true using differentiation for first principles.

    02:18 And as mathematicians, we like proofs because that shows us that what we're doing is the truth.


    About the Lecture

    The lecture Differentiation Basics by Batool Akmal is from the course Calculus Methods: Differentiation.


    Author of lecture Differentiation Basics

     Batool Akmal

    Batool Akmal


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