Higher Order Derivatives

JEE Main Mathematics · Methods of Differentiation · 11 questions, latest first

• 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)+∫_0^2…20264 April, Shift 1 · Q17
• Let f(x)=x^3+x^2 f^′(1)+2 x f^′ ′(2)+f^′ ′ ′(3), x ∈ R. Then the value of f^′(5) is:202621 January, Shift 2 · Q17
• If log_e y=3 sin^-1 x, then (1-x^2) y^′ ′-x y^′ at x=1/2 is equal to20249 April, Shift 2 · Q8
• Let 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 a^2+b^2+c^2 is equal to:20249 April, Shift 1 · Q6
• If y(θ)=(2 cos θ+ cos 2 θ)/(cos 3 θ+4 cos 2 θ+5 cos θ+2), then at θ=(π)/2, y^′ ′+y^′+y is equal to:20245 April, Shift 2 · Q20
• 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 to202429 January, Shift 2 · Q9
• Let f(x)=x^3+x^2 f^′(1)+x f^′ ′(2)+f^′ ′ ′(3), x ∈ R. Then f^′(10) is equal to ____.202427 January, Shift 1 · Q25
• Let f(x)=(sin x+ cos x-√2)/(sin x- cos x), x ∈[0, π]-{(π)/4}. Then f((7 π)/12) f^′ ′((7 π)/12) is equal to20238 April, Shift 1 · Q19
• If f(x)=x^2+g^′(1) x+g^′ ′(2) and g(x)=f(1) x^2+x f^′(x)+f^′ ′(x), then the value of f(4)-g(4) is equal to ____.20231 February, Shift 1 · Q81
• Let y(x)=(1+x)(1+x^2)(1+x^4)(1+x^8)(1+x^16). Then y^′-y^′ ′ at x=-1 is equal to:202325 January, Shift 1 · Q68
• If f(x)=x^3-x^2 f^′(1)+x f^′ ′(2)-f^′ ′ ′(3), x ∈ R, then202324 January, Shift 2 · Q71