Question:

Let y=e²x. Then ((d²y)/(dx²))((d²x)/(dy²)) is:

Show Hint

Use inverse differentiation identities carefully.

Updated On: Mar 20, 2026

\(1\)
\(e^{-2x}\)
\(2e^{-2x}\)
-2e⁻2x

Hide Solution

Verified By Collegedunia

The Correct Option is A

Solution and Explanation

Step 1: (dy)/(dx)=2e²x, (d²y)/(dx²)=4e²x
Step 2: (dx)/(dy)=\frac12e²x, (d²x)/(dy²)=-\frac14e⁴x
Step 3: ((d²y)/(dx²))((d²x)/(dy²)) =4e²x·\frac14e²x=1

Was this answer helpful?

0

0

Top Questions on Second Order Derivative

If $t = e^{2x}$ and $y = \ln(t^2)$, then $\frac{d^2 y}{dx^2}$ is:
- CUET (UG) - 2024
- Mathematics
- Second Order Derivative
View Solution
The second-order derivative of which of the following functions is $5^x$?
- CUET (UG) - 2024
- Mathematics
- Second Order Derivative
View Solution
Given the equation: \[ y = (\tan^{-1} 2x)^2 + (\cot^{-1} 2x)^2, \] find the expression: \[ (1+4x^2)^2 y'' - 16. \]
- AP EAMCET - 2024
- Mathematics
- Second Order Derivative
View Solution
The function \(y=e^{kr}\) satisfies \((\frac{d^2y}{dx^2}+\frac{dy}{dx})(\frac{dy}{dx}-y)=y\frac{dy}{dx}\). It is valid for
- WBJEE - 2023
- Mathematics
- Second Order Derivative
View Solution
Let $f$ be a twice differentiable function on $R$.
If $f ^{\prime}(0)=4$ and $f(x)+\int\limits_0^x(x-t) f^{\prime}(t) d t=\left(e^{2 x}+e^{-2 x}\right) \cos 2 x+\frac{2}{a} x,$
then $(2 a+1)^5 a^2$ is equal to ______.
- JEE Main - 2023
- Mathematics
- Second Order Derivative
View Solution

View More Questions

Questions Asked in BITSAT exam

View More Questions