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If y=xln x for x>0, then (d^2y)/(dx^2 at x=2 is Single correct option
If
y = x ln x y=x\ln x y = x ln x for
x > 0 x>0 x > 0 , then
d 2 y d x 2 \dfrac{d^2y}{dx^2} d x 2 d 2 y at
x = 2 x=2 x = 2 is
A. 2 2 2 B. 1 2 \dfrac12 2 1 C. ln 2 + 1 \ln2+1 ln 2 + 1 D. 1 1 1 Show answer and solution Answer: (B) 1 2 \dfrac12 2 1
y ′ = ln x + 1 y'=\ln x+1 y ′ = ln x + 1 by the product rule, and
y ′ ′ = 1 x y''=\frac1x y ′′ = x 1 . At
x = 2 x=2 x = 2 ,
y ′ ′ = 1 2 y''=\frac12 y ′′ = 2 1 . The value
ln 2 + 1 \ln2+1 ln 2 + 1 is
y ′ y' y ′ at
x = 2 x=2 x = 2 ,
1 1 1 is the coefficient of
ln x \ln x ln x in
y ′ y' y ′ , and
2 2 2 inverts the result. Differentiate twice, then substitute.
Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake