JEE Main 2024 — Differentiation Questions with Solutions

If f(x)= \arraylx³ ((1)/(x) ), x ≠ 0 \ 0 , x=0array . then

If y(θ)=(2 θ+ 2 θ)/( 3 θ+4 2 θ+5 θ+2), then at θ=(π)/(2), yⁱme ⁱme+yⁱme+y is equal to :

Suppose for a differentiable function h, h(0)=0, h(1)=1 and hⁱme(0)=hⁱme(1)=2. If g(x)=h (e^x ) eh⁽x⁾, then gⁱme(0) is…

Let f(x)=a x³+b x²+c x+41 be such that f(1)=40, fⁱme(1)=2 and fⁱme(1)=4. Then a²+b²+c² is equal to:

Let y = log e 1 - x 2 1 + x 2 , - 1 < x < 1 . Then at x = 1 2 , the value of 225 y ' - y " is equal to

Let f ( x ) = x 3 + x 2 f ' ( 1 ) + x f " ( 2 ) + f ''' ( 3 ) , x ∈ R . Then f ' ( 10 ) is equal to

If e y=3 ⁻¹ x, then (1-x² ) yⁱme ⁱme-x yⁱme at x=(1)/(2) is equal to

If y = x + 1 x 2 − x x x + x + x + 1 15 3 cos 2 x − 5 cos 3 x , then 96 y ' π 6 is equal to:

Let for a differentiable function f : ( 0 , ∞ ) → R , f x - f y ≥ log e x y + x - y , ∀ x , y ∈ 0 , ∞ . Then ∑ n = 1 20…

Let f(x)=x⁵+2 ex / ⁴ for all x R. Consider a function g(x) such that (g ° f)(x)=x for all x R. Then the value of 8 gⁱme…