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Differentiation of Logs: Example

by Batool Akmal
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      DLM Differentiation of Exponential and Logarithmic Functions Calculus Akmal.pdf
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    So we've looked at the rules of logs. We'll now going back to differentiating, so rules of logs are important for us when we need to use them. We'll see as they come up in different questions. But if we start to look at differentiating ln's and we'll start with an example and then we?ll build up from there. So the first question here is asking us to differentiate ln of 5x cubed plus 7x minus 11. We've been ask to differentiate this so we'll have to remind ourselves how to differentiate ln of x. So just on the side, hopefully this is going to our minds that to differentiate ln of x, dy/dx, that gives you an answer of 1/x. And remember that this is ln of x, gives you 1/x. Okay, so if it's ln of something else, you'll get 1 over something else. Let's look at our function for a moment. We have ln, but it's not ln of x, it's ln of something on the inside. So the first thing that we need to acknowledge is this is a function inside of a function. We have this function here, which is inside of an ln function, so we're going to apply the chain rule. Step by step, we do dy/dx, the first thing that we need to do is just differentiate ln. So ln of anything is just 1 over that thing. So because this is unjust, you can treat this as your x. So ln of x, but instead of ln of x, we've got ln of 5x cubed, plus 7x minus 11. So we can say 1 over 5x cubed plus 7x minus 11. So ln of 5x cubed, plus 7x minus 11, differentiates to 1 over exactly the same thing without changing it....

    About the Lecture

    The lecture Differentiation of Logs: Example by Batool Akmal is from the course Differentiation of Exponential and Logarithmic Functions.


    Author of lecture Differentiation of Logs: Example

     Batool Akmal

    Batool Akmal


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