Continuity and Differentiability notes
OpenThe 4 formulas you need for Continuity and Differentiability, on one page.
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Maths · printable
Continuity and Differentiability: One-Page Formula Sheet
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Last updated: 26 October 2026
Formula sheet
Continuity and Differentiability formulas
Continuity and Differentiability — formula sheet
Formulas
- Chain rule: d/dx f(g(x)) = f′(g(x))g′(x)
- Parametric: dy/dx = (dy/dt)/(dx/dt)
- Logarithmic differentiation for xˣ type functions
- d/dx (sin⁻¹x) = 1/√(1 − x²)
Key ideas
- Continuous at a: LHL = RHL = f(a)
- Differentiable implies continuous, not the reverse
- |x| is continuous but not differentiable at 0
- Greatest integer function is discontinuous at integers
Traps to avoid
- Checking only one side
- Assuming continuity means differentiability
- Wrong derivative of inverse trig functions
jeevisionary.in/jee-topics/maths/continuity-differentiability/
FAQs
Frequently asked questions
Where can I get a Continuity and Differentiability formula sheet PDF for free?
On this page. Use the print button and choose 'Save as PDF'.
How should I use a formula sheet?
Read it once a day for a week, then cover it and write the formulas from memory. Revise only the ones you missed.