Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Differentiation

NDA 2023 · Mathematics · Differentiation

If f^ (x)= ( x) and y f( array ll 2 & 3 array ) , then what is (d...

If f′(x)=cos⁡(ln⁡x)f^{\prime}(x)=\cos (\ln x) and y \quad f\left(23\begin{array}{ll}2 & 3\end{array}\right), then what is dydx\frac{d y}{d x} equal to?

Options

  1. Acos⁡(ln⁡(2x−3x))\cos \left(\ln \left(\frac{2 x-3}{x}\right)\right)
  2. B−3x2sin⁡(ln⁡(2x−3x))-\frac{3}{x^2} \sin \left(\ln \left(\frac{2 x-3}{x}\right)\right)
  3. C3x2cos⁡(ln⁡(2x−3x))\frac{3}{x^2} \cos \left(\ln \left(\frac{2 x-3}{x}\right)\right)
  4. D−3x2cos⁡(ln⁡(2x−3x))-\frac{3}{x^2} \cos \left(\ln \left(\frac{2 x-3}{x}\right)\right)

Correct answer

C. 3x2cos⁡(ln⁡(2x−3x))\frac{3}{x^2} \cos \left(\ln \left(\frac{2 x-3}{x}\right)\right)

Step-by-step solution

Since, y=f(2x−3x)⇒dydx=\mathrmf′(2x−3x)⋅ddx(2x−3x)y=f\left(\frac{2 x-3}{x}\right)\Rightarrow \quad \frac{\mathrm{dy}}{\mathrm{dx}}=\mathrmf^{\prime}\left(\frac{2 \mathrm{x}-3}{\mathrm{x}}\right) \cdot \frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{2 \mathrm{x}-3}{\mathrm{x}}\right)⇒dydx=f′(2x−3x)⋅(3x2)...(i)⇒dydx=3x2cos⁡(ln⁡(2x−3x))\begin{aligned} & \Rightarrow \quad \frac{d y}{d x}=f^{\prime}\left(\frac{2 x-3}{x}\right) \cdot\left(\frac{3}{x^2}\right) ...(i)\\ & \Rightarrow \quad \frac{d y}{d x}=\frac{3}{x^2} \cos \left(\ln \left(\frac{2 x-3}{x}\right)\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 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