COMEDK · Maths · 23. Inverse Trigonometric Functions
If \(y=\tan ^{-1}\left(\frac{a-x}{1+a x}\right)\), then \(\frac{d y}{d x}=\)
- A \(\frac{1}{\left(1+x^{2}\right)}\)
- B \(\frac{a}{\left(1+a x^{2}\right)}\)
- C \(-\frac{1}{\left(1+x^{2}\right)}\)
- D \(\frac{x}{\left(1+x^{2}\right)}\)
Answer & Solution
Correct Answer
(C) \(-\frac{1}{\left(1+x^{2}\right)}\)
Step-by-step Solution
Detailed explanation
Given, \(y=\tan ^{-1}\left(\frac{a-x}{1+a x}\right)\) \[ \Rightarrow \quad y=\tan ^{-1} a-\tan ^{-1} x \] Taking derivative w.r.t. \(x\) on both sides, we get \[ \frac{d y}{d x}=-\frac{1}{1+x^{2}} \]
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The complex number \(\dfrac{1+7 i}{(2-i)^2}\) lies inCOMEDK 2025 Medium
- In the group \((1,2,3,4,5,6)\) under multiplication \(7,2^{-1} \times 4\) is equal toCOMEDK 2013 Medium
- Three vertices are chosen randomly from the eight vertices of a regular 8-sided polygon. The probability that they form the vertices of an isosceles triangle, isCOMEDK 2023 Medium
- Set \(P=\{x: x\) is a multiple of 4 less than 40\(\}\)
\(Q=\{x: x\) is an odd multiple of 7 less than 50\(\}\)
\(R=\{x: x\) is a multiple of 6 less than 50\(\}\)
Then \(n(P \cup Q \cup R)=\)COMEDK 2025 Medium - \(\text { If } y=\sqrt{\sin x+y} \text { then find } \dfrac{d y}{d x} \text { at } x=0, \quad y=1\)COMEDK 2024 Medium
- In the parabola \(y^2=4 a x\) the length of the latus rectum is 6 units and there is a chord passing through its vertex and the negative end of the latus rectum. Then the equation of the chord isCOMEDK 2024 Medium
More PYQs from COMEDK
- An air bubble in water \(\left(\mu=\dfrac{4}{3}\right)\) is shown in figure. The apparent depth of the image of the bubble in plane mirror viewed by observer is.
COMEDK 2023 Medium - \(\int \frac{\sin x + \cos x}{\sqrt{1 + 2 \sin x \cos x}} dx = \varphi(x) + C\) (assuming \(\sin x + \cos x > 0\)). Then \(\varphi(x) =\)COMEDK 2025 Easy
- \(\text { The function } y=\tan x-x \text { is }\)COMEDK 2024 Easy
- Emission of electrons from a metal plate illuminated with monochromatic electromagnetic radiation will always take place providedCOMEDK 2025 Easy
- Let \(a\) and \(b\) be non-zero real such that \(a \neq b\).
Then, the equation of the line passing through the origin and the point of intersection of \(\frac{x}{a}+\frac{y}{b}=1\) and \(\frac{x}{b}+\frac{y}{a}=1\) isCOMEDK 2015 Medium - Evaluate the value of the arbitrary constant ' c ' given that \(\mathrm{y}(0)=0\), of the differential equation \(\dfrac{d y}{d x}+\dfrac{x y}{x^2-1}=\dfrac{x^6+4 x}{\sqrt{1-x^2}}\)COMEDK 2025 Medium