Match List I with List II
| LIST I | LIST II | ||
| A. | $\frac{dy}{dx}$ for $y^3-3xy^2=x^3+3x^2y$ | I. | $x(5+6log \, x)$ |
| B. | $\frac{dy}{dx}$ for $y=x^x$ | II. | $\frac{2log x-3}{x^3}$ |
| C. | $\frac{d^2y}{dx^2}$ for $y=\frac{log\, x}{x}$ | III. | $y(1+log x)$ |
| D. | $\frac{d^y}{dx^2}$ for $y=x^3log x$ | IV. | $\frac{(x+y)^2}{y^2-2xy-x^2}$ |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A-IV, B-III, C-II, D-I
(A) $3y^2\frac{dy}{dx}-3y^2-6xy\frac{dy}{dx}=3x^2+3x^2\frac{dy}{dx}+6xy$
$⇒\frac{dy}{dx}=\frac{(x+y)^2}{y^2-2xy-x^2}$
(B) $\frac{dy}{dx}=\frac{d(x^x)}{dx}=y(1+\log x)$
(C) $\frac{dy}{dx}=\frac{1-\log x}{x^2}⇒\frac{d^2y}{dx^2}=\frac{2\log x-3}{x^2}$
(D) $\frac{dy}{dx}=3x^2\log x+x^2=x(1+3x\log x)$