TS EAMCET · Maths · Differentiation
If \(y=x+\tan x\), then \(\cos ^2 x \frac{d^2 y}{d x^2}+2 x\) is equal to
- A -2 y
- B \(\frac{2}{3} y\)
- C 3y
- D 2y
Answer & Solution
Correct Answer
(D) 2y
Step-by-step Solution
Detailed explanation
Given, \(y=x+\tan x\) Differentiating, \(\frac{d y}{d x}=1+\sec ^2 x\) Again differentiating, \(\frac{d^2 y}{d x^2}=0+2 \sec x \sec x \tan x\) \[ =2 \sec ^2 x \cdot \tan x \] Now, \(\cos ^2 x \cdot \frac{d^2 y}{d x^2}+2 x=\cos ^2 x \cdot 2 \sec ^2 x \cdot \tan x+2 x\)…
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
- Let and . If is the acute angle between the lines and thenTS EAMCET 2022 Easy
- If \({ }^n P_r=30240\) and \({ }^n C_r=252\), then the ordered pair \((n, r)\) is equal toTS EAMCET 2008 Easy
- \[ \int_0^2 \frac{x}{(2-x)^{\frac{3}{4}}} d x= \]TS EAMCET 2023 Medium
- If the lengths of the perpendiculars drawn from a point \((a, b)\) to the lines \(2 x+3 y+4=0\) and \(3 x-3 y+4=0\) are same, then the point \((a, b)\) lies on the lineTS EAMCET 2022 Medium
- If at any point \(\left(x_1, y_1\right)\) on the curve \(y=f(x)\) the lengths of the subtangent and subnormal are equal, then the length of the tangent drawn to that curve at that point isTS EAMCET 2019 Easy
- \(I_{m, n}=\int x^m(\log x)^n d x=\)TS EAMCET 2020 Easy
More PYQs from TS EAMCET
- Which of the following is not correct?TS EAMCET 2007 Easy
- If \(2 x+y=0\) is the equation of a chord of the circle \(x^2+y^2-2 x-6 y+3=0\), then the circle with this chord as diameter passes through the pointTS EAMCET 2020 Easy
- The volume of one mole of the gas is changed from \(V\) to \(2 V\) at constant pressure \(p\). If \(\gamma\) is the ratio of specific heats of the gas, change in internal energy of the gas isTS EAMCET 2014 Easy
- The length of the segment of the tangent line to the curve \(x=a \cos ^3 t, y=\alpha \sin ^3 t\), at any point on the curve cut off by the coordinate axes isTS EAMCET 2016 Hard
- If \(\frac{42-13 x}{x^2+x-6}=\frac{\mathrm{A}}{l x+m}+\frac{\mathrm{B}}{p x+q}\) where \(l m>0\) and \(p q < 0\) then \(\frac{\mathrm{A} l p}{\mathrm{~B} m q}=\)TS EAMCET 2022 Medium
- Young's modulus experiment is performed on a steel wire of \(1 \mathrm{~m}\) length and \(8 \mathrm{~mm}\) diameter. The mass required to be added in the experiment to produce \(5 \mathrm{~mm}\) elongation of the wire is \(\left(Y_{\text {steel }}=2 \times 10^9 \mathrm{Nm}^{-2}, g=10 \mathrm{~m} / \mathrm{s}^2\right)\)TS EAMCET 2018 Easy