Question
Differentiate the following w.r.t. x:

$\tan ^{-1}\left[\sqrt{\frac{\sqrt{1+x^2+x}}{\sqrt{1+x^2}-x}}\right]$

Answer

Get the step-by-step solution for this question inside the Vidyadip app.

Get the answer in the app

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

If $\cos^{-1}\frac{\text{x}}{2}+\cos^{-1}\frac{\text{y}}{3}=\alpha,$ then prove that $9\text{x}^2-12\text{xy}\cos\alpha+4\text{y}^2=36\sin^2\alpha.$
The probabilities of two students A and B coming to the school in time are $\frac{3}{7}$ and $\frac{5}{7}$ respectively. Assuming that the events, 'A coming in time' and 'B coming in time' are independent, find the probability of only one of them coming to the school in time. Write at least one advantage of coming to school in time.
The total area of a page is $150 cm^2$. The combined width of the margin at the top and bottom is$ 3 \ cm$ and the side $2 \ cm .$ What must be the dimensions of the page in order that the area of the printed matter may be maximum?
A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below:
Type of Toys
Machine
 
I
II
III
A
12
18
6
B
6
0
9
Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs. 7.50 and that on each toy of type B is Rs. 5, show that 15 toys of type A and 30 toys of type B should be manufactured in a day to get maximum profit.
Evaluate the following integrals:
$\int \frac{\text{x}^2}{(\text{x}-1)\sqrt{\text{x}+2}}\text{ dx}$
Evaluate : $\int \sqrt{\frac{x-5}{x-7}} \cdot d x$
If $\begin{bmatrix}\text{x}&4&1\end{bmatrix}\begin{bmatrix}2&1&2\\1&0&2\\0&2&-4\end{bmatrix}\begin{bmatrix}\text{x}\\4\\-1\end{bmatrix}=0,$ find x.
If $\text{x}=\text{a}\sin\text{t}-\text{b}\cos\text{t},\text{y}=\text{a}\cos\text{t}+\text{b}\sin\text{t},$ Prove that $\frac{\text{d}^2\text{y}}{\text{dx}^2}=-\frac{\text{x}^2+\text{y}^2}{\text{y}^2}$
Represent the following families of curves by forming the corresponding differential equation:
$\text{x}^2+\text{y}^2=\text{ax}^3$
Evaluate the following integrals:$\int^\limits1_0\frac{1-\text{x}^2}{\text{x}^4+\text{x}^2+1}\text{ dx}$