Method of Differentiation
Higher Order Derivatives
JEE Main 2019
Grade 12
Question:
If $e^y(x + 1) = 1$, then $\frac{d^2y}{dx^2}$ equals:
(1) $\left(\frac{dy}{dx}\right)^2$
(2) $-\left(\frac{dy}{dx}\right)^2$
(3) $\frac{dy}{dx}$
(4) $-\frac{dy}{dx}$
Step-by-Step Solution
Key Concept: Take the logarithm of the given relation to write $y = -\ln(x + 1)$, which makes both derivatives very quick to compute and compare.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)