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

• January 12th 2010, 06:45 PM
ckoeber
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.
• January 12th 2010, 07:59 PM
Dark Sun
Let $f(t)=\sqrt{t+\sqrt t}$, and let F(t) be an antiderivative of f(t). Then;
$\int _0^{\tan x}\sqrt{t+\sqrt t} dt=F(t)]_0^{\tan x}=F(\tan x)-F(0).$
$\frac{d}{dx}\int _0^{\tan x}\sqrt{t+\sqrt t} dt=F'(\tan x)\cdot \sec ^2 x-F'(0)=\sqrt{\tan x+\sqrt{\tan x}}\cdot \sec ^2x$.