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Math Help - Checking on an answer Finding the derivative of a square root.

  1. #1
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    Checking on an answer Finding the derivative of a square root.

    So, I am working on finding the derivative of the following function:

    Using the chain rule I did the following:

    My two questions are:
    1. Is this right?

    2. If correct, should I leave it in this form?
    Thank you so much for your time.
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  2. #2
    Junior Member Dark Sun's Avatar
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    The answer I got was:

    Let f(t)=\sqrt{t+\sqrt t}, and let F(t) be an antiderivative of f(t). Then;

    \int _0^{\tan x}\sqrt{t+\sqrt t} dt=F(t)]_0^{\tan x}=F(\tan x)-F(0).

    So, by the chain rule:

     \frac{d}{dx}\int _0^{\tan x}\sqrt{t+\sqrt t} dt=F'(\tan x)\cdot \sec ^2 x-F'(0)=\sqrt{\tan x+\sqrt{\tan x}}\cdot \sec ^2x.
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  3. #3
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    I see, you did the substitutions that I didn't do. I'll rework the problem and check back!

    Thanks again.
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