TS EAMCET · Maths · Differentiation
If \(y=\tan ^{-1}\left(\frac{3 x-x^3}{1-3 x^2}\right)+\tan ^{-1}\left(\frac{4 x-4 x^3}{1-6 x^2+x^4}\right)\) then \(\frac{d y}{d x}\) is equal to
- A \(\frac{2}{1+x^2}\)
- B \(\frac{4}{1+x^2}\)
- C \(\frac{6}{1+x^2}\)
- D \(\frac{7}{1+x^2}\)
Answer & Solution
Correct Answer
(D) \(\frac{7}{1+x^2}\)
Step-by-step Solution
Detailed explanation
We have, \[ y=\tan ^{-1}\left(\frac{3 x-x^3}{1-3 x^2}\right)+\tan ^{-1}\left(\frac{4 x-4 x^3}{1-6 x^2+x^4}\right) \] Put \(x=\tan \theta\), we get…
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 diameters of a circle are along \(2 x+y-7=0\) and \(x+3 y-11=0\). Then, the equation of this circle, which also passes through \((5,7)\), isTS EAMCET 2009 Easy
- If \(\frac{x+1}{\left(x^2+1\right)(x-1)^2}=\frac{A x+B}{x^2+1}+\frac{C}{x-1}+\frac{D}{(x-1)^2}\), then \(\mathrm{A}+\mathrm{B}+\mathrm{C}+\mathrm{D}=\)TS EAMCET 2023 Medium
- The diameter of a sphere is measured as \(42 \mathrm{~cm}\). If there is an error of \(1 / 77 \mathrm{~cm}\) in measuring it, then the error involved in the volume of that sphere (in cubic centimeters) isTS EAMCET 2023 Medium
- If a group of six students including two particular students A and B stand in a row, then the probability of getting an arrangement in which A and B are separated by exactly one student in between them isTS EAMCET 2023 Medium
- Let \(\left|\begin{array}{ccc}x^2+x+1 & x+1 & 2 x-3 \\ 3 x^2-1 & x+2 & x-1 \\ x^2+5 x+1 & 2 x+3 & x+4\end{array}\right|\) \(=a x^4+b x^3+c x^2+d x+e\) be an identity in \(x\). If \(a, b, c, d\) are known, then the value of \(e\) isTS EAMCET 2015 Easy
- If \(\tan \theta+\tan \left(\theta+\frac{\pi}{3}\right)+\tan \left(\theta+\frac{2 \pi}{3}\right)=3\), then which of the following is equal to 1 ?TS EAMCET 2008 Medium
More PYQs from TS EAMCET
- If \(X\) is a poisson variate such that \(\alpha=P(X=1)=P(X=2)\), then \(P(X=4)\) is equal toTS EAMCET 2012 Medium
- If \(x=\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}\), then \(x^2(x-4)^2\) is equal to :TS EAMCET 2006 Hard
- \(x_1, x_2 \in \mathbf{N}\). If a line having slope 2 is a tangent to the curve \(y=x^4-6 x^3+13 x^2-10 x+5\) at points \(P\left(x_1, y_1\right)\) and \(Q\left(x_2, y_2\right)\), then \(x_1 x_2+y_1 y_2=\)TS EAMCET 2020 Easy
- Two diodes are connected in the following fashion. Provision is made to connect either \(+5 \mathrm{~V}\) or ground \((0 \mathrm{~V})\) to the points \(A\) to \(B\). The output \(Q\) will act as
TS EAMCET 2019 Hard - If \(\sin \mathrm{A}=-\frac{24}{25}, \cos \mathrm{~B}=\frac{15}{17}, \mathrm{~A}\) does not belong to \(4^{\text {th }}\) quadrant and B does not belong to \(1^{\text {st }}\) quadrant then \((\mathrm{A}+\mathrm{B})\) lies in the quadrantTS EAMCET 2025 Medium
- Sodium is heated in air at \(300^{\circ} \mathrm{C}\) to form \(X . X\) absorbs \(\mathrm{CO}_2\) and forms \(\mathrm{Na}_2 \mathrm{CO}_3\) and \(Y\). Which of the following is \(Y\) ?TS EAMCET 2005 Easy