Derivative of sin(x)

by Batool Akmal

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    So let's get straight into it now, we are now going to derive the answer for the gradient of sin x. We already know the answer to this, I know. So we've discussed already that sin x differentiate the cos of x but we're going to prove it to ourselves, we're gonna develop our algebraic, our proving, our analysis skills a little bit more and we're hopefully going to be excited when we see the answer. So back to the very first lecture of differentiation from first principles, let me just remind you every time we're faced by a function that we want to prove, we can always go back to the definition of the derivative. So if I remind you, if you have, dy/dx of a function, you say limit delta x tends to zero of f of x plus delta x minus f of x over delta x. We are now trying to prove sin of x so we want the derivative of sin of x as the limit of delta x tends to zero. Okay, so instead of using f, we'll now use s, sin of x plus delta x minus the original sin x all over delta x. Right, we can start using our addition law, so if you look at this function here, this is basically sin a plus b. So you can compare this with sin a plus b that we looked up previously, so your a is your x and b is your delta x. So we can use that identity to expand this. We said that sin a plus b is sin a cos b plus sin b cos a but in this case we'll obviously do this with x's and deltas. So we got sin x cos delta x plus sin...

    About the Lecture

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

    Included Quiz Questions

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

    Author of lecture Derivative of sin(x)

     Batool Akmal

    Batool Akmal

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