Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Differentiation

JEE Advanced · Mathematics · Differentiation

If y= a^2-b^2 ^2( x) then x^2 y^2 ((d y)/(d x))^2 is equal to

If y=a2−b2cos⁡2(ln⁡x)theny=\sqrt{a^2-b^2 \cos ^2(\ln x)} thenx^2 y^2(dydx)2\left(\frac{d y}{d x}\right)^2 is equal to

Options

  1. Aa2−y2a^2-y^2
  2. B(a2−y2)(b2−a2+y2)\left(a^2-y^2\right) \left(b²-a²+y²\right)
  3. Ca2+b2−y2a^2+b^2-y^2
  4. D(b2−y2)(a2−b2y2)\left(b^2-y^2\right) \left(a²-b² y²\right)

Correct answer

C. a2+b2−y2a^2+b^2-y^2

Step-by-step solution

y2=a2−b2cos⁡2(ln⁡x)⇒2ydydx=2b2cos⁡(ln⁡x)sin⁡(ln⁡x)⋅1x∴x2y2(dydx)2=b4cos⁡2(ln⁡x)sin⁡2(ln⁡x)=b4(a2−y2b2)(1−a2−y2b2)\begin{aligned} & y^2=a^2-b^2 \cos ^2(\ln x) \Rightarrow 2 y \frac{d y}{d x}=2 b^2 \cos (\ln x) \sin (\ln x) \cdot \frac{1}{x} \\ & \therefore x^2 y^2\left(\frac{d y}{d x}\right)^2=b^4 \cos ^2(\ln x) \sin ^2(\ln x)=b^4\left(\frac{a^2-y^2}{b^2}\right)\left(1-\frac{a^2-y^2}{b^2}\right)\end{aligned}
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 Most Important Selected Qs for JEE Advanced PYQs