Download App

CONTINUITY AND DIFFERENTIABILITY — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSCONTINUITY AND DIFFERENTIABILITY2 Marks
Question
Find the second order derivatives of the function given in Exercise:
$\tan^{-1}\text{x}$
✓

Answer

Let $\text{y}=\tan^{-1}\text{x}$
$\therefore\ \frac{\text{dy}}{\text{dx}}=\frac{1}{1+\text{x}^2}$
and $\frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{(1+\text{x}^2).0-1.2\text{x}}{(1+\text{x}^2)^2}=-\frac{2\text{x}}{(1+\text{x}^2)^2}$

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 "2 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

Let $A = \{a, b, c, d\}$ and $f : A \rightarrow A$ be given by $f = \{(a, b), (b, d), (c, a), (d, c)\}.$ Write $f ^{-1}.$
→
A factory produces bulbs. The probability that one bulb is defective is $\frac{1}{50}$ and they are packed in boxes of 10. From a single box, find the probability that. 
exactly two bulbs are defective.
→
Differentiate the ${e^x} + {e^{{x^2}}} + ... + {e^{{x^5}}}$ w.r.t. x.
→
If A and B are two events such that $\text{P}(\text{A}\cap\text{B})=0.32$ and P (B) = 0.5, find $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)$.
→
Evaluate $\int\frac{\text{x}^2+4\text{x}}{\text{x}^3+6\text{x}^2+5}\text{ dx}$
→
Given two independent events A and B such that P(A) = 0.3 and P(B) = 0.6. Find
$\text{P}(\text{A}\cap\overline{\text{B}})$
→
Which of the following distributions of a random variable X are the probability distributions?
X: 0 1 2 3 4
P(X): 0.1 0.5 0.2 0.1 0.1
→
Evaluate the following integrals:
$\int\cos^{-1}(\sin\text{x})\text{dx}$
→
Find the antiderivative $F (x)$ of the function defined by $f(x)=5 x^4-5$ where $F (0)=2$.
→
Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$2\frac{\text{d}^2\text{y}}{\text{dx}^2}+3\sqrt{1-\Big(\frac{\text{dy}}{\text{dx}}\Big)^2-\text{y}}=0$
→