If x-e^ + x^2+1 2 , find dy dx - Vidyadip

Question

If $\text{x}-\text{e}^{\tan\text{x}}+\sqrt{\frac{\text{x}^2+1}{2}},$ find $\frac{\text{dy}}{\text{dx}}$

✓

Answer

$\text{y}=\text{x}^{\tan\text{x}}+\sqrt{\frac{\text{x}^2+1}{2}}$
$\text{y}=\text{e}^{\tan\text{x}\log\text{x}}+\text{e}^{\frac{1}{2}\log\big(\frac{\text{x}^2+1}{2}\big)}$
$\frac{\text{dy}}{\text{dx}}=\text{e}^{\tan\text{x}\log\text{x}}\frac{\text{d}}{\text{dx}}(\tan\text{x}\log\text{x})+\text{e}^{\frac{1}{2}\log\big(\frac{\text{x}^2+1}{2}\big)}\frac{\text{d}}{\text{dx}}\Big(\frac{1}{2}\log\Big(\frac{\text{x}^2+1}{2}\Big)\Big)$
$\frac{\text{dy}}{\text{dx}}=\text{e}^{\tan\text{x}}\Big[\frac{\tan\text{x}}{\text{x}}+\sec^3\text{x}\log\text{x}\Big]+\sqrt{\frac{\text{x}^2+1}{2}}\Big(\frac{1}{2}\times\frac{2}{\text{x}^2+1}\times(\text{x})\Big)$
$\frac{\text{dy}}{\text{dx}}=\text{e}^{\tan\text{x}}\Big[\frac{\tan\text{x}}{\text{x}}+\sec^3\text{x}\log\text{x}\Big]+\sqrt{\frac{\text{x}^2+1}{2}}\Big(\frac{\text{x}}{\text{x}^2+1}\Big)$
$\frac{\text{dy}}{\text{dx}}=\text{e}^{\tan\text{x}}\Big[\frac{\tan\text{x}}{\text{x}}+\sec^3\text{x}\log\text{x}\Big]+\frac{\text{x}}{\sqrt{2(\text{x}^2+1)}}$

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

Explore more

More "5 Marks Questions" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\text{A}=\begin{bmatrix}1&2\\2&1\end{bmatrix}, f(x) = x^2 - 2x - 3,$ show that $f(A) = 0$

Show that for any two vectors $\vec a $ and $\vec b$ , we always have $|\vec{a}+\vec{b}| \leq|\vec{a}|+|\vec{b}|$ (triangle inequality).

Evaluate the following:
$\sin\Big(\sec^{-1}\frac{17}{8}\Big)$

If $x=\sin ^{-1}\left(\frac{2 t}{1+t^2}\right), y=\cos ^{-1}\left(\frac{1-t^2}{1+t^2}\right)$ then find $\frac{d y}{d x}$.

$\text{If x = a} (\cos 2\text{t +2t}\sin \text{2t}) \text{and y = a} (\sin \text{2t - 2t}\cos\text{2t}),\text{then find}\frac{\text{d}^{2}{\text{y}}}{\text{dx}^{2}}.$

Find the distance of a point $(2,4,-1)$ from the line $\frac{x+5}{1}=\frac{y+3}{4}=\frac{z-6}{-9}$.

In the following, find the value of the constant k so that the given function is continuous at the indicated point:
$\text{f(x)}=\begin{cases}(\text{x}-1)\tan\frac{\pi\text{x}}{2},&\text{if}\text{ x}\neq1\\\text{k},&\text{if}\text{ x}=1\end{cases}\text{at x} = 1$

Of the students in a school, it is known that $30\%$ have $100\%$ attendanceand $70\%$ students are irregular. Previous year results report that $70\%$ of all students who have $100\%$ attendance attain A grade and $10\%$ irregular students attain A grade in their annual examination. At the end of the year, one student is chosen at random from the school and he was found to have an A grade. What is the probability that the student has $100\%$ attendance? Is regularity required only in school? Justify your answer.

Solve the following systems of linear equations by cramer's rule:

2x + ay = 2, $\text{a}\neq0$

Solve the following differential equation:$\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}=\text{x}\text{e}^{\text{x}}$