Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Differentiation

NDA 2012 · Mathematics · Differentiation

If y= (e^ m x +e^ -m x ) , then what is (d y)/(d x) at x=0 equal to?

If y=ln⁡(emx+e−mx)y=\ln \left(e^{m x}+e^{-m x}\right), then what is dydx\frac{d y}{d x}at x=0x=0 equal to?

Options

  1. A-1
  2. B0
  3. C1
  4. D2

Correct answer

B. 0

Step-by-step solution

y=\log _e\left(e^{m x}+e^{-m x}\right)\frac{d y}{d x}=\frac{1}{\left(e^{m x}+e^{-m x}\right)} \cdot\left(e^{m x} \cdot m+e^{-m x}(-m)\right)=\frac{1}{\left(e^{m x}+e^{-m x}\right)}\left(e^{m x}-e^{-m x}\right)\left(\frac{d y}{d x}\right)_{x=0}=0
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 2024Paragraph: Let f:(-1,1) arrow R be a differentiable function with f(0)=-1 and f^ (0)=1 .… 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 2023 Full Differentiation list Differentiation JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs