Derivative of tan(x)

by Batool Akmal

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    And now, the last one. Let?s just prove the answer or the differential of tan x. We know that we should be getting minus sec squared x but let?s try it out using exactly the same method. So, if you enjoyed the previous two proofs, I recommend that you try it yourself and then just catch up and check with us once you?re done. Okay, so we?re going to derive the answer for tan of x. Again, we?re going to use differentiation from first principles or the definition of a derivative. We?re saying as the limit of delta x tends to zero is f of x plus delta x minus the original function, all over delta x. This time, our function is tan of x. So, we are differentiating that. Also remember, eventually we?re going to take the limit of delta x to zero. So we can rewrite this as tan of x plus delta x, minus the original function tan of x all over delta x. So we?re going to have to expand this using the addition law for tan. That?s a little bit more complicated than the others but we?ll just have to use a little bit of algebra to tweak it and make it a little bit tidier. So, if you recall that we can compare this with the tan of A plus B. So our A now is x and the B is delta x, and you just apply the same formula. Looking back at the formula, we find out that this expands to tan x not A. So, tan x plus tan delta x over 1 minus tan x tan delta x. Don?t forget, we have to take tan x away from it as well, and that it?s all being divided by delta x and...

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

    Author of lecture Derivative of tan(x)

     Batool Akmal

    Batool Akmal

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