JEE Main Mathematics — Differentiation Previous-Year Questions

Let f(x) and g(x) be twice differentiable functions satisfying f''(x) = g''(x) for all x R, f'(1) = 2g'(1) = 4 and g(2)…

Let f be a real polynomial of degree n such that f(x) = f'(x) f''(x), for all x R. If f(0) = 0, then 36 (f'(2) + f''(2)…

Let f(x)=x³+x² fⁱme(1)+2 x fⁱme ⁱme(2)+fⁱme ⁱme ⁱme(3), x R. Then the value of fⁱme(5) is:

Let f: R → R be a twice differentiable function such that ( x y)(f(2 x+2 y)-f(2 x-2 y))=( x y)(f(2 x+2 y)+f(2 x-2 y)),…

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