Mathematics · 2013
JEE Main · 23 April 2013, Shift 1 · Q78
If f(x)= sin ( sin x) and f^′ ′(x)+ tan x f^′(x)+ g (x)=0, then g (x) is:
If $\displaystyle f(x)=\sin (\sin x)$ and
$\displaystyle f^{\prime \prime}(x)+\tan x f^{\prime}(x)+\mathrm{g}(x)=0$, then $\displaystyle \mathrm{g}(x)$ is :
Official answer
(4)
$\displaystyle \cos ^2 x \sin (\sin x)$
More from Methods of Differentiation
- Let f(x)=( sin ( tan^-1 x)+ sin ( cot^-1 x))^2-1, |x|>1. If (d y)/(d x)=1/2 d/(d x)( sin^-1(f(x))) and y(√3)=(π)/6, then y(-√3) is equal to:2020
- If y(x)=x^x, x>0, then y^′ ′(2)-2 y^′(2) is equal to:2023
- If x^2+y^2+ sin y=4, then the value of (d^2 y)/(d x^2) at the point (-2, 0) is:2018
- If 2 x^y+3 y^x=20, then (d y)/(d x) at (2,2) is equal to:2023
- Let f(x)= log_e( sin x),(0<x<π) and g(x)= sin^-1(e^-x),(x ≥ 0). If α is a positive real number such that a=(f_° g)^′(α) and b=(f ° g)(α), then:2019
- If f(x)= sin^-1((2 × 3^x)/(1+9^x)), then f^′(-1/2) equals:2018
- If y(x)=(x^x)^x, x>0, then (d^2 x)/(d y^2)+20 at x=1 is equal to \ \ \ \.2022
- Suppose for a differentiable function h, h(0)=0, h(1)=1 and h^′(0)=h^′(1)=2. If g(x)=h(e^x) e^h(x), then g^′(0) is equal to:2024
JEE Main 2013 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.