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.
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.
The answer I got was:
Let $\displaystyle f(t)=\sqrt{t+\sqrt t}$, and let F(t) be an antiderivative of f(t). Then;
$\displaystyle \int _0^{\tan x}\sqrt{t+\sqrt t} dt=F(t)]_0^{\tan x}=F(\tan x)-F(0).$
So, by the chain rule:
$\displaystyle \frac{d}{dx}\int _0^{\tan x}\sqrt{t+\sqrt t} dt=F'(\tan x)\cdot \sec ^2 x-F'(0)=\sqrt{\tan x+\sqrt{\tan x}}\cdot \sec ^2x$.