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

JEE Main · Mathematics · Differentiation

If y=a x+(5+2 x) x , then y^ +y=

If y=asin⁡x+(5+2x)cos⁡xy=a \sin x+(5+2 x) \cos x, then y′′+y=y^{\prime \prime}+y=

Options

  1. A4cos⁡x4 \cos x
  2. B−4cos⁡x-4 \cos x
  3. C4sin⁡x4 \sin x
  4. D−4sin⁡x-4 \sin x

Correct answer

D. −4sin⁡x-4 \sin x

Step-by-step solution

y=asin⁡x+(5+2x)cos⁡xy=a \sin x+(5+2 x) \cos x Differential w.r.t ' xx ' y′=acos⁡x+(5+2x)(−sin⁡x)+(0+2)cos⁡xy′=acos⁡x−(5+2x)sin⁡x+2cos⁡x\begin{aligned} & y^{\prime}=a \cos x+(5+2 x)(-\sin x)+(0+2) \cos x \\ & y^{\prime}=a \cos x-(5+2 x) \sin x+2 \cos x \end{aligned} Again differential w.r.t ' xx ' y′′=−asin⁡x−[(5+2x)cos⁡x+(0+2)sin⁡x]+2(−sin⁡x)⇒y′′=−asin⁡x−(5+2x)cos⁡x−2sin⁡x−2sin⁡x⇒y′′=−(asin⁡x+(5+2x)cos⁡x)−4sin⁡x⇒y′′=−y−4sin⁡x⇒y′′+y=−4sin⁡x\begin{aligned} & y^{\prime \prime}=-a \sin x-[(5+2 x) \cos x \\ & \quad+(0+2) \sin x]+2(-\sin x) \\ & \Rightarrow y^{\prime \prime}=-a \sin x-(5+2 x) \cos x-2 \sin x-2 \sin x \\ & \Rightarrow y^{\prime \prime}=-(a \sin x+(5+2 x) \cos x)-4 \sin x \\ & \Rightarrow y^{\prime \prime}=-y-4 \sin x \\ & \Rightarrow y^{\prime \prime}+y=-4 \sin x \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 99 Percentile Qs Bank for JEE Main PYQs