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 $\vec a,\vec b,\vec c$ are unit vectors such that $\vec a + \vec b + \vec c = 0$ find the value of $\vec a.\vec b + \vec b.\vec c + \vec c.\vec a$.

Find one-parameter families of solution curves of the following differential equation: (or solve the following differential equation)$\frac{\text{dy}}{\text{dx}}-\frac{2\text{xy}}{1+\text{x}^2}=\text{x}^2+2$

Show that the lines $\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ and $\frac{x-2}{1}=\frac{y+4}{3}=\frac{z-6}{5}$ intersect each other. Find also the coordinates of the point of intersection.

If $\text{x}\sqrt{1+\text{y}}+\text{y}\sqrt{1+\text{x}}=0,$ prove that $(1+\text{x})^2\frac{\text{dx}}{\text{dx}}+1=0$

Decompose the vector $6\hat{\text{i}}-3\hat{\text{j}}-6\hat{\text{k}}$ into vectors which are parallal and perpendicular to the vector $\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}.$

Find the vector equation of the following planes in non-parametric form.
$\vec{\text{r}}=(2\hat{\text{i}}+2\hat{\text{j}}-\hat{\text{k}})+\lambda(\hat{\text{i}}+2\hat{\text{j}}+3\hat{\text{k}})+\mu(5\hat{\text{i}}-2\hat{\text{j}}+7\hat{\text{k}})$

Two cards are drawn simultaneously (without replacement) from a well-shuffled pack of 52 cards. Find the mean and variance of the number of red cards.

If $\text{y}=\log\frac{\text{x}^2+\text{x}+1}{\text{x}^2-\text{x}+1}+\frac{2}{\sqrt{3}}\tan^{-1}\Big(\frac{\sqrt{3}\text{x}}{1-\text{x}^2}\Big),$ find $\frac{\text{dy}}{\text{dx}}$

Solve the following differential equations:$\text{cosec x}\log\text{y}\frac{\text{dy}}{\text{dx}}+\text{x}^2\text{y}^2=0$

Find the probability distribution of the number of doublets in three throws of a pair of dice and find its mean.