CBSE · Class 6-12

Class 12 · Mathematics (041)

Unit 5 · Class 12Mathematics (041)

Calculus

Continuity and Differentiability

Continuity at a point and on an interval, differentiability, chain rule, and derivatives of implicit/parametric/logarithmic functions.

Lessons

4 concepts

1
Continuity
$f$ is continuous at $a$ iff $\lim_{x \to a} f(x) = f(a)$ .
2
Chain Rule
$\dfrac{dy}{dx} = \dfrac{dy}{du} \cdot \dfrac{du}{dx}$ .
3
Implicit & Parametric
Differentiate both sides w.r.t. $x$ ; for parametric $x = f(t), y = g(t)$ : $\dfrac{dy}{dx} = \dfrac{g'(t)}{f'(t)}$ .
4
Logarithmic Differentiation
Take $\ln$ of both sides for expressions like $y = x^x$ .

Skills to practise

Skill · medium

Continuity and Differentiability — Practice (coming soon)

Practice bank for this unit is in progress. You can still read the lessons above.