Derivative of cos(x)

by Batool Akmal

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    So if you enjoyed the proof for sin x, now is your chance to take the lead on the proof for cos x. It?s very similar to what we?ve just done with the same methods. It?s incredible that we?ve learnt these derivatives all through school but we?ve never really seen where they come from and now is your chance to actually prove it to yourselves. So, using exactly the same method, let?s now find the derivative for cos x. Remember, we kind of, not kind of we do know the answer to this already but let?s see if we can actually derive it algebraically. So, once again using differentiation from first principles, we are saying that dy/dx as the limit of delta x tends to zero is f of x plus delta x minus f of x divided by delta x. This time, we are differentiating cos x or we?re finding what the derivative of cos x is. So, that?s what we?re trying to do as the limit of delta x tends to zero. So, we can rewrite this as cos x plus delta x minus the original cos x all over delta x. This functional now, we will need to expand using our double angle or addition law formulas that we gave right at the start. So, remember that you can compare this with cos of a plus b. So this is the same as cos of a plus b and you can look that rule up and actually use that to expand cos x plus delta x. So, if we expand this using our rule, we can say cos x cos delta x. This time we have a minus sin x sin delta x minus cos x over delta x is our differentiation from first principles. Again, we...

    About the Lecture

    The lecture Derivative of cos(x) by Batool Akmal is from the course Differentiation of Trigonometric Functions.

    Included Quiz Questions

    1. -sin(x)
    2. sin(x)
    3. -cos(x)
    4. tan(x)

    Author of lecture Derivative of cos(x)

     Batool Akmal

    Batool Akmal

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