✓ Board-verified
Mathematics · 2026 · 2 marks
Continuity and DifferentiabilityDerivatives of Functions in Parametric Forms2 marksApplyvery short answer
CBSE 2026 · Region 2 · Set 2 · Q25
If x= sin t - cos t, y = sin t cos t, find dy/(d x) at t =(π)/4.
If $\displaystyle x=\sin \mathrm{t}-\cos \mathrm{t}, \mathrm{y}=\sin \mathrm{t} \cos \mathrm{t}$, find $\displaystyle \frac{\mathrm{dy}}{\mathrm{d} x}$ at $\displaystyle \mathrm{t}=\frac{\pi}{4}$.
Marking-scheme solution
$\displaystyle x=\sin t-\cos t \Rightarrow \dfrac{dx}{dt}=\cos t+\sin t$
$\displaystyle \mathrm{y}=\sin t \cos t \Rightarrow \dfrac{dy}{dt}=-\sin^{2} t+\cos^{2} t$
$\displaystyle \dfrac{dy}{dx}=\dfrac{-\sin^{2} t+\cos^{2} t}{\cos t+\sin t}$ or $\displaystyle \cos t-\sin t$
$\displaystyle \therefore \left.\dfrac{dy}{dx}\right]_{t=\frac{\pi}{4}}=0$
All Continuity and Differentiability questions2026 question paperNCERT solutions: Continuity and DifferentiabilityPractice Continuity and Differentiability →
More from Continuity and Differentiability
- The derivative of sin (x^2) w.r.t. x, at x=√π is:2024
- The value of k for which function f(x)= {x^2, x ≥ 0; kx, x<0} is differentiable at x=0 is:2023
- If f(x)= {(sin^2 a x)/(x^2), x ≠ 0; 1, x=0} is continuous at x=0, then the value of a is:2025
- Differentiate y=√(log { sin ((x^3)/3-1)}) with respect to x.2025
- If y=(cos x- sin x)/(cos x+ sin x), then (d y)/(d x) is:2023
- If f(x)= {(log (1+a x)+ log (1-b x))/x, for x ≠ 0; k, for x=0} is continuous at x=0, then the value of k is:2025
- Differentiate sec^-1(1/(√(1-x^2))) w.r.t. sin^-1(2 x √(1-x^2)). OR If y= tan x+ sec x, then prove that (d^2 y)/(d x^2)=(cos x)/((1- sin x)^2).2023
- If f(x)= {(x^2-4 x-5)/(x+1), x ≠-1; k, x=-1} is continuous at x=-1, then the value of k is:2026
CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.