MHT CET · Maths · Differentiation
If \(y=\tan ^{-1}\left(\frac{2+3 x}{3-2 x}\right)+\tan ^{-1}\left(\frac{4 x}{1+5 x^2}\right)\), then \(\frac{\mathrm{d} y}{\mathrm{~d} x}=\)
- A \(\frac{1}{1+25 x^2}\)
- B \(\frac{5}{1+25 x^2}\)
- C \(\frac{1}{1+5 x^2}\)
- D \(\frac{5}{1+5 x^2}\)
Answer & Solution
Correct Answer
(B) \(\frac{5}{1+25 x^2}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & y=\tan ^{-1}\left(\frac{2+3 x}{3-2 x}\right)+\tan ^{-1}\left(\frac{4 x}{1+5 x^2}\right) \\ & =\tan ^{-1}\left(\frac{\frac{2}{3}+x}{1-\frac{2}{3} x}\right)+\tan ^{-1}\left(\frac{5 x-x}{1+5 x^2}\right) \\ & =\tan ^{-1} \frac{2}{3}+\tan ^{-1} x+\tan ^{-1} 5 x-\tan ^{-1} x \\ \therefore \quad & y=\tan ^{-1} \frac{2}{3}+\tan ^{-1} 5 x \\ \therefore \quad & \frac{d y}{d x}=\frac{1}{1+(5 x)^2} \cdot 5=\frac{5}{1+25 x^2}\end{aligned}\)
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 micro-organisms double themselves in 3 hours. Assuming that the quantity increases at a rate proportional to it self, then the number of times it multiplies themselves in 18 years isMHT CET 2020 Medium
- The principal increases continuously in a newly opened bank at the rate of \(10 \%\) per year. An amount of Rs. 2000 is deposited with this bank. How much will it become after 5 years? \(\left(e^{0.5}=1.648\right)\)MHT CET 2025 Medium
- If \(\mathrm{A}\left[\begin{array}{ll}2 & 1 \\ 7 & 4\end{array}\right]\) then \(\left(\mathrm{A}^2-5 \mathrm{~A}\right)^{-1}\) isMHT CET 2024 Medium
- If \(x=2 \cos \theta-\cos 2 \theta\) and \(y=2 \sin \theta-\sin 2 \theta\), then \(\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}\) is equal toMHT CET 2024 Medium
- If \(y=2 x\) is a chord of circle \(x^2+y^2-10 x=0\), then the equation of circle with this chord as diameter isMHT CET 2021 Medium
- Suppose A is any \(3 \times 3\) non-singular matrix and \((\mathrm{A}-3 \mathrm{I})(\mathrm{A}-5 \mathrm{I})=0\) where \(\mathrm{I}=\mathrm{I}_3\) and \(\mathrm{O}=\mathrm{O}_3\). Here \(\mathrm{O}_3\) represent zero matrix of order 3 and \(\mathrm{I}_3\) is an identity matrix of order 3 . If \(\alpha \mathrm{A}+\beta \mathrm{A}^{-1}=4 \mathrm{I}\), then \(\alpha+\beta\) is equal toMHT CET 2024 Medium
More PYQs from MHT CET
- Which of the following are the pulse points of the lower limb?
I. Brachial\(\quad\)II. Radial
III. Posterior tibial\(\quad\)IV. Dorsalis pedis
V. Femoral\(\quad\)VI. Popliteal
Select the correct optionMHT CET 2025 Hard - A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to retail store. Then the probability that the store will receive at most one defective bulb isMHT CET 2023 Easy
- Calculate van't Hoff factor of aqueous solution of 0.18 m electrolyte that freezes at \(-0.54^{\circ} \mathrm{C}\)
\(\left(\mathrm{K}_{\mathrm{f}} \text { for solvent }=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\)MHT CET 2025 Medium - The vector sum of two forces \(\overrightarrow{\mathrm{A}}\) and \(\overrightarrow{\mathrm{B}}\) is perpendicular to their vector difference. Hence forces \(\vec{A}\) and \(\vec{B}\) areMHT CET 2025 Medium
- How many optical isomers are possible for a compound having four asymmetric carbon atoms?MHT CET 2020 Easy
- If \(y=\left(\sin ^{-1} x\right)^2+\left(\cos ^{-1} x\right)^2\), then \(\left(1-x^2\right) y_2-x y_1=\)MHT CET 2023 Hard