Differentiate the following functions with respect to x: ( ^ -1 x… - Vidyadip

Question

Differentiate the following functions with respect to x:
$\log(\tan^{-1}\text{x})$

✓

Answer

Consider $\text{y}=\log\big(\tan^{-1}\text{x}\big)$
Differentiate with respect to x,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\log\big(\tan^{-1}\text{x}\big)$
$=\frac{1}{\tan^{-1}\text{x}}\times\frac{\text{d}}{\text{dx}}\big(\tan^{-1}\text{x}\big)$
[Using chain rule]
$=\frac{1}{\big(1+\text{x}^2\big)\tan^{-1}\text{x}}$
Hence, the solution is, $\frac{\text{d}}{\text{dx}}\big(\log\tan^{-1}\text{x}\big)=\frac{1}{\big(1+\text{x}^2\big)\tan^{-1}\text{x}}$

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 "Solve the Following Question.(3 Marks)" from Differentiation→Differentiation — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Solve the differential equation $\frac{d y}{d x}+y=e^{-x}$

Check the commutativity and associativity of the following binary operations:
$'*'$ on Q defined by a * $b =( a - b )^2$ for $all a , b \in Q$.

Prove the following results:
$\tan^{-1}\frac{2}{3}=\frac{1}{2}\tan^{-1}\frac{12}{5}$

Discuss the continuity of the following functions at the indicated point:
$\text{f}\text{(x)}=\begin{cases}(\text{x}-\text{a}){\sin}\Big(\frac{1}{\text{x}-\text{a}}\Big) & \text{x} \neq \text{a}\\\ 0, & \text{ x} = \text{a}\end{cases}\text{at x}=\text{a}$

Let A = [-1, 1]. Then, discuss whether the following functions from A to itself are one-one, onto or bijective:
$\text{f(x)}=\frac{\text{x}}{2}$

Construct the composition table for $\times _5$ on $Z_5 = {0, 1, 2, 3, 4}$.

Find the vector equation of the plane passing through the origln and containing the line

$\bar{r}=(\hat{i}+4 \hat{j}+\hat{k})+\lambda(\hat{i}+2 \hat{j}+\hat{k})$.

For what value of k is the following function continuous at x = 2?
$\text{f(x)}=\begin{cases}2\text{x}+1,&\text{if }\text{ x}<2\\\text{k},&\text{x}=2\\3\text{x}-1,&\text{x}>2\end{cases}$

Find the probability that in 10 throws of a fair die, a score which is a multiple of 3 will be obtained in at least 8 of the throws.

Evaluate the following intregals:
$\int\frac{1}{\cos2\text{x}+3\sin^2\text{x}}\ \text{dx}$