Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Differentiation

NDA 2024 · Mathematics · Differentiation

Paragraph: Let f:(-1,1) arrow R be a differentiable function with...

Paragraph: Let f:(−1,1)→Rf:(-1,1) \rightarrow \mathrm{R} be a differentiable function with f(0)=−1f(0)=-1 and f′(0)=1f^{\prime}(0)=1. Let h(x)=f(2f(x)+2)h(x)=f(2 f(x)+2) and g(x)=(h(x))2g(x)=(h(x))^2.
Question: What is \mathrmh′(0)\mathrmh^{\prime}(0) equal to?

Options

  1. A-2
  2. B-1
  3. C0
  4. D2

Correct answer

D. 2

Step-by-step solution

Let f:(−1,1)→R\mathrm{f}:(-1,1) \rightarrow \mathrm{R} be a differentiable function with f(0)=−1andf′(0)=1h(x)=f(2f(n)+2)\mathrm{f}(0)=-1 and f^{\prime}(0)=1h(x)=f(2 f(n)+2) Differentiate both side w.r.t xxh′(x)=f′(2f(x)+2)2f′(x)h′(0)=f′(2f(0)+2)⋅2f′(0)=f′(−2+2)⋅2(1)=f′(0)⋅2=(1)⋅2=2[∵f(0)=−1 and  f′(0)=1]\begin{aligned} & h^{\prime}(x)=f^{\prime}(2 f(x)+2) 2 f^{\prime}(x) \\ & h^{\prime}(0)=f^{\prime}(2 f(0)+2) \cdot 2 f^{\prime}(0)=f^{\prime}(-2+2) \cdot 2(1) \\ & =f^{\prime}(0) \cdot 2=(1) \cdot 2=2\left[\because f(0)=-1 \text{\text{ and } } f^{\prime}(0)=1\right] \end{aligned}$$
Practice Differentiation on Quantrex Academy →

More from Differentiation

Passage: Let (e^y)^x-y=0 , where y is a function of x whose domain is (0,10] . Question… NDA 2026If [4] y =x+ x^2+4 , then what is x^2+4 \,(dy)/(dx) equal to ? NDA 2026Passage: Let (e^y)^x-y=0 , where y is a function of x whose domain is (0,10] . Question… NDA 2026For the following two (02) items: Consider the function f(x) = cases 4(5^x), & x What is… NDA 2025Consider the following for the two (02) items that follow: Let x = θ - θ and y = ^4θ… NDA 2025Consider the following for the two (02) items that follow: Let (x+y)^ p+q = x^p y^q… NDA 2025Consider the following for the two (02) items that follow: Let y = ^ -1 (x… NDA 2025For the following three (03) items: Let y = f(x) = x ^ -1 x 1 - x^2 + 1 - x^2 . If x = θ… NDA 2025Consider the following for the two (02) items that follow: Let (x+y)^ p+q = x^p y^q… NDA 2025For the following three (03) items: Let y = f(x) = x ^ -1 x 1 - x^2 + 1 - x^2 . What is… NDA 2025Consider the following for the two (02) items that follow: Let x = θ - θ and y = ^4θ… NDA 2025Paragraph: Let f:(-1,1) arrow R be a differentiable function with f(0)=-1 and f^ (0)=1 .… NDA 2024Let f(x) and g(x) be two functions such that g(x)=x-(1)/(x) and f o g(x)=x^3-(1)/(x^3) .… NDA 2024Let a function f be defined on ℝ-\ 0\ and 2 f(x)+f((1)/(x))=x+3 If f is differentiable… NDA 2023If f(x)=| | x| | where 0 < x < 1 , then what is f^ (0.5) equal to? NDA 2023If f^ (x)= ( x) and y f( array ll 2 & 3 array ) , then what is (d y)/(d x) equal to? NDA 2023 Full Differentiation list Differentiation JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs