Continuity and Differentiability

CBSE Class 12 · Mathematics · 41 past questions

14 of 41 · show all

1. Q2 2026

   If $e^{-x}+e^{-y}=2$, then $\frac{dy}{dx}$ is

   Try it →
2. Q7 2026

   If $\sin^{-1} x = y$, then $\frac{dy}{dx}$ is…

   Try it →
3. Q10 2026

   If $(\sin x)^y=y^{\cos x}$, then find $\frac{dy}{dx}$.

   Try it →
4. Q14 2025

   Differentiate $2^{\cos^2 x}$ w.r.t. $\cos^2 x$.

   Try it →
5. Q18 2025

   If $x = e^{x/y}$, then prove that $\frac{dy}{dx} = \frac{x - y}{x \log x}$.

   Try it →
6. Q26 2024

   The derivative of $\sin(x^2)$ w.r.t. $x$, at $x = \sqrt{\pi}$ is…

   Try it →
7. Q29 2024

   The derivative of $2^x$ w.r.t. $3^x$ is…

   Try it →
8. Q30 2024

   If $x\cos(p+y)+\cos p\sin(p+y)=0$, prove that $\cos p\,\frac{dy}{dx} = -\cos^2(p+y)$, where p is a constant.

   Try it →
9. Q32 2024

   The derivative of $\tan^{-1}(x^2)$ w.r.t. $x$ is…

   Try it →
10. Q33 2024

    If $f(x) = |\tan 2x|$, then find the value of $f'(x)$ at $x = \dfrac{\pi}{3}$.

    Try it →
11. Q36 2023

    If $y = \frac{\cos x - \sin x}{\cos x + \sin x}$, then $\frac{dy}{dx}$ is…

    Try it →
12. Q37 2023

    If $y = x^{\frac{1}{x}}$, then find $\frac{dy}{dx}$ at $x = 1$.

    Try it →
13. Q39 2023

    If $y = (x + \sqrt{x^2 - 1})^2$, then show that $(x^2 - 1)\left(\frac{dy}{dx}\right)^2 = 4y^2$.

    Try it →
14. Q41 2023

    If $\tan\left(\frac{x+y}{x-y}\right) = k$, then $\frac{dy}{dx}$ is equal to

    Try it →