TS EAMCET · Maths · Differentiation
If \(f(x)=\frac{1}{1+\frac{1}{x}}\) and \(g(x)=\frac{1}{1+\frac{1}{f(x)}}\), then \(g^{\prime}(2)\) is equal to
- A \(\frac{1}{5}\)
- B \(\frac{1}{25}\)
- C \(5\)
- D \(\frac{1}{16}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{25}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \quad f(x)=\frac{1}{1+\frac{1}{x}}=\frac{x}{1+x} \\ & \text { and } \quad g(x)=\frac{1}{1+\frac{1}{f(x)}}=\frac{1}{1+\frac{1+x}{x}}=\frac{x}{2 x+1} \\ & \therefore \quad g^{\prime}(x)=\frac{(2 x+1) \cdot 1-x(2)}{(2 x+1)^2}=\frac{1}{(2 x+1)^2} \\ & \text { Now,…
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 general solution of \(\frac{d y}{d x}=\frac{x+y+1}{y-x+1}\) isTS EAMCET 2020 Easy
- The equation of the plane in cartesian form, which is at a distance of \(\frac{6}{\sqrt{29}}\) from the origin and its normal vector drawn from the origin being \(2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}\), isTS EAMCET 2019 Easy
- If and are the roots of the equation where are rational numbers, then the roots of the equation areTS EAMCET 2022 Easy
- The general solution of the differential equation \(x^2 d y\) \(-\left(x y-y^2\right) d x=0\) isTS EAMCET 2023 Medium
- If the probability that an individual will suffer a bad reaction from an injection is then the probability that out of individuals, exactly individuals suffer a bad reaction isTS EAMCET 2021 Easy
- If \(x=\log \left(y+\sqrt{y^2+1}\right)\) then \(y=\)TS EAMCET 2023 Medium
More PYQs from TS EAMCET
- Which of the following statement is not true?TS EAMCET 2017 Easy
- Which one of the following is the ratio of the lowering of vapour pressure of \(0.1 \mathrm{M}\) aqueous solutions of \(\mathrm{BaCl}_2, \mathrm{NaCl}\) and \(\mathrm{Al}_2\left(\mathrm{SO}_4\right)_3\) respectively?TS EAMCET 2011 Easy
- Let \(f(x)\) be differentiable on \([1,6]\) and \(f(1)=-2\). If \(f(x)\) has only one root in \((1,6)\) then there exists \(\mathcal{C} \in(1,6)\) such thatTS EAMCET 2018 Easy
- A deflection magnetometer is adjusted and a magnet of magnetic moment \(M\) is placed on it in the usual manner and the observed deflection is \(\theta\). The period of oscillation of the needle before settling of the deflection is \(T\). When the magnet is removed, the period of oscillation of the needle is \(T_0\) before settling to \(0^{\circ}-0^{\circ}\). If the earth's induced magnetic field is \(B_H\), the relation between \(T\) and \(T_0\) isTS EAMCET 2013 Hard
- Identify the correct statements from the following: (a) In Orthoboric acid, boron is in planar geometry. (b) In , boron has tetrahedral geometry. (c) Aqueous solution of borax is acidic.TS EAMCET 2018 Medium
- White metal is an alloy ofTS EAMCET 2015 Medium