If x = 1-t/1+t and y = 3t/1+t, then d^2y/dx^2 is equal to Option 1: 1/1+t^2 Option 2: 0 Option 3: -1 Option 4: -1/1+t^2

The answer is '0'. View full solution:

Calculus > Continuity & Differentiability

Medium

core

If $x = \frac{1-t}{1+t}$ and $y = \frac{3t}{1+t}$, then $\frac{d^2y}{dx^2}$ is equal to

$\frac{1}{1+t^2}$

-1

$\frac{-1}{1+t^2}$

✅ Correct Option: 2

Related questions:

2025: 21 May Shift 1

If $f(x) = \begin{cases} \frac{\tan(\frac{\pi}{4} - x)}{\cot 2x} & , x ≠ \frac{\pi}{4} \\ 2K + 1 & , x = \frac{\pi}{4} \end{cases}$ is continuous at $x = \frac{\pi}{4}$ , then the value of K is equal to

2026: 18th May Shift 2

If $y=\sqrt[5]{\log_e(5x^2)}$ , then $\dfrac{dy}{dx}=$

(Take $\log_e x=\log x$ )

2025: 3 June Shift 2

If $\sin y = x \cos(a + y)$ , then $\frac{dy}{dx}$ is equal to

2026: 26th May Shift 2

If $y = (\log_e x)^{\log_e x}$ , then $\dfrac{dy}{dx}$ is equal to:

2022: 4 Aug Shift 1

If $y = \frac{\sqrt{x+1} + \sqrt{x-1}}{\sqrt{x+1} - \sqrt{x-1}}$ , then $(x^2-1)^{3/2} \frac{d^2y}{dx^2} =$

2026: 18th May Shift 2

For the function $(ex)^y=e^x$ ;

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. $y$ is equal to	I. $\dfrac{1-\log_e x}{x(1+\log_e x)^3}$
B. value of $\dfrac{dy}{dx}$	II. $\dfrac{x}{1+\log_e x}$
C. value of $\dfrac{d^2y}{dx^2}$	III. $\dfrac{\log_e x}{(1+\log_e x)^2}$
D. $x^y$ is equal to	IV. $e^{x-y}$

Choose the correct answer from the options given below:

If $x = \frac{1-t}{1+t}$ and $y = \frac{3t}{1+t}$, then $\frac{d^2y}{dx^2}$ is equal to

Keyboard Shortcuts