Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Differentiation

NTA Abhyas 2020 · Mathematics · Differentiation

If f(x) = x - 4 x - 4 + ta n ^ - 1 ((1 - 2x)/(2 + x)), 4 < x < 8,...

If f(x)=x−4x−4+tan−1(1−2x2+x),∀4<x<8,f\left(x\right) = \sqrt{x - 4\sqrt{x - 4}} + ta{n}^{- 1}\left(\dfrac{1 - 2x}{2 + x}\right), \forall 4 < x < 8, then the value of f′(5){\text{f}}^{′} \left(5\right) is equal to

Options

  1. A−713- \dfrac{7}{13}
  2. B00
  3. C513\dfrac{5}{13}
  4. D−813- \dfrac{8}{13}

Correct answer

A. −713- \dfrac{7}{13}

Step-by-step solution

f(x)=(x−4)2+22−2.2x−4+tan⁡−1(12−x1+12.x)f\left(x\right) = \sqrt{{\left(\sqrt{x - 4}\right)}^{2} + {2}^{2} - 2.2\sqrt{x - 4}} + \tan^{- 1}\left(\dfrac{\dfrac{1}{2} - x}{1 + \dfrac{1}{2} . x}\right)
f(x)=(x−4−2)2+tan⁡−112−tan⁡−1xf\left(x\right) = \sqrt{{\left(\sqrt{x - 4} - 2\right)}^{2}} + \tan^{- 1}\dfrac{1}{2} - \tan^{- 1}x
f(x)=2−x−4+tan−1(12)−tan⁡−1x(∵x−4<2)f\left(x\right) = 2 - \sqrt{x - 4} + ta{n}^{- 1}\left(\dfrac{1}{2}\right) - \tan^{- 1}x\left(∵ \sqrt{x - 4} < 2\right)
f′(x)=−12x−4−11+x2{\text{f}}^{′} \left(\text{x}\right) = \dfrac{- 1}{2\sqrt{\text{x} - 4}} - \dfrac{1}{1 + {\text{x}}^{2}}
f′(5)=−12−11+25=−1426=−713{\text{f}}^{′} \left(5\right) = \dfrac{- 1}{2} - \dfrac{1}{1 + 25} = \dfrac{- 14}{26} = - \dfrac{7}{13}
Practice Differentiation on Quantrex Academy →

More from Differentiation

Let ℝ denote the set of all real numbers. Consider the polynomial function f: ℝ arrow ℝ… JEE Advanced 2026Let f(x) and g(x) be twice differentiable functions satisfying f''(x) = g''(x) for all x… JEE Main 2026Let f be a real polynomial of degree n such that f(x) = f'(x) f''(x) , for all x ∈ ℝ . If… JEE Main 2026Let f(x)=x^ 3 +x^ 2 f^ (1)+2 x f^ (2)+f^ (3), x ∈ R . Then the value of f^ (5) is: JEE Main 2026Let ℝ denote the set of all real numbers. Let f: ℝ arrow ℝ and g: ℝ arrow(0,4) be… JEE Advanced 2025Let f: R arrow R be a twice differentiable function such that ( x y)(f(2 x+2 y)-f(2 x-2… JEE Main 2025If _e y=3 ^ -1 x , then (1-x^2) y^ -x y^ at x=(1)/(2) is equal to JEE Main 2024Let f(x)=a x^3+b x^2+c x+41 be such that f(1)=40, f^ (1)=2 and f^ (1)=4 . Then… JEE Main 2024Suppose for a differentiable function h, h(0)=0, h(1)=1 and h^ (0)=h^ (1)=2 . If… JEE Main 2024If f(x)=\ array l x^3 ((1)/(x)), x ≠ 0 0 , x=0 array . then JEE Main 2024If y(θ)=(2 θ+ 2 θ)/( 3 θ+4 2 θ+5 θ+2) , then at θ=(π)/(2), y^ +y^ +y is equal to : JEE Main 2024Let f(x)=x^5+2 e^ x / 4 for all x ∈ R . Consider a function g(x) such that (g ∘ f)(x)=x… JEE Main 2024If y = ( x + 1)( x ^ 2 - x ) x x + x + x + (1)/(15)(3 ^ 2 x - 5) ^ 3 x, then 96 y ^ '… JEE Main 2024Let y = _ e ( 1 - x ^ 2 1 + x ^ 2 ), - 1 < x < 1 . Then at x = (1)/(2) , the value of… JEE Main 2024Suppose f(x) = ( 2 ^ x + 2 ^ - x ) x ^ - 1 ( x ^ 2 - x + 1) (7 x ^ 2 + 3x + 1) ^ 3 . Then… JEE Main 2024Let f ( x ) = x ^ 3 + x ^ 2 f ^ ' ( 1 ) + x f ^ " ( 2 ) + f ^ ''' ( 3 ) , x ∈ R . Then f… JEE Main 2024 Full Differentiation list Differentiation JEE Maths PYQsJEE Mathematics PYQs All NTA Abhyas JEE Main PYQs