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Continuity and Differentiability Maths Formulas for Class 12 Chapter 5

Are you looking for Continuity and Differentiability formulas for class 12 Chapter 5? Today, we are going to share Continuity and Differentiability formulas for class 12 Chapter 5 according to student requirements. You are not a single student who is searching for Continuity and Differentiability formulas for class 12 chapters 2. According to me, thousands of students are searching Continuity and Differentiability formulas for class 12 Chapter 5 per month. If you have any doubt or issue related to Continuity and Differentiability formulas then you can easily connect with through social media for discussion. Continuity and Differentiability formulas will very helpful to understand the concept and questions of the chapter Continuity and Differentiability.

  1. Properties related to the functions:
    • (i) \((f\pm g) (x) = f (x)\pm g(x)\) is continuous.
    • (ii) \((f.g)(x) = f (x) .g (x)\) is continuous.
    • (iii) \(\frac{f}{g}(x) = \frac{f(x)}{g(x)}\) (whenever \(g(x)\neq 0\) is continuous.
  2. Chain Rule: If f = v o u, t = u (x) and if both \(\frac{\mathrm{d} t}{\mathrm{d} x}\) and \(\frac{\mathrm{d} v}{\mathrm{d} x}\) exists, then:
    \(\frac{\mathrm{d} f}{\mathrm{d} x}=\frac{\mathrm{d} v}{\mathrm{d} t}.\frac{\mathrm{d} t}{\mathrm{d} x}\)
  3. Rolle’s Theorem: If f: [a, b] → R is continuous on [a, b] and differentiable on (a, b) where as f(a) = f(b), then there exists some c in (a, b) such that f ′(c) = 0.
  4. Mean Value Theorem: If f : [a, b] → R is continuous on [a, b] and differentiable on (a, b). Then there exists some c in (a, b) such that
    \(f'(c)=\frac{f(b)-f(a)}{b-a}\)
Derivative Formulas
\(\frac{\mathrm{d} }{\mathrm{d} x}(sin^{-1}x)\) \(\frac{1}{\sqrt{1-x^2}}\)
\(\frac{\mathrm{d} }{\mathrm{d} x}(cos^{-1}x)\) \(-\frac{1}{\sqrt{1-x^2}}\)
\(\frac{\mathrm{d} }{\mathrm{d} x}(tan^{-1}x)\) \(\frac{1}{1+x^2}\)
\(\frac{\mathrm{d} }{\mathrm{d} x}(cot^{-1}x)\) \(\frac{-1}{1+x^2}\)
\(\frac{\mathrm{d} }{\mathrm{d} x}(sec^{-1}x)\) \(\frac{1}{x\sqrt{1-x^2}}\)
\(\frac{\mathrm{d} }{\mathrm{d} x}(cosec^{-1}x)\) \(\frac{-1}{x\sqrt{1-x^2}}\)
\(\frac{\mathrm{d} }{\mathrm{d} x}(e^x)\) \(e^x\)
\(\frac{\mathrm{d} }{\mathrm{d} x}(log\:x)\) \(\frac{1}{x}\)

 

Summary of Continuity and Differentiability formulas

We have listed top important formulas for Continuity and Differentiability for class 12 Chapter 5 which is help support to solve questions related to the chapter Continuity and Differentiability. i would like to say that after remembering the Continuity and Differentiability formulas you can start the questions and answers solution of the Continuity and Differentiability chapter. If you faced any problem to find solution of Continuity and Differentiability questions, please let me know through commenting or mail.

Maths Formulas for Class 12 by Chapters

Here Check Maths formulas for class 12 by chapter wise.

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