Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

Differentiation forms the basis of calculus, and we need its formulas to solve problems.

We have prepared a list of all the Formulas


Basic Differentiation Formulas

Basic Differentiation Formulas.jpg

Differentiation of Log and Exponential Function

Differentiation of Log and Exponential Function.jpg

Differentiation of Trigonometry Functions


Differentiation of Inverse Trigonometry Functions

Differentiation of Inverse Trigonometry Functions.jpg

Differentiation Rules

Differentiation Rules.jpg

  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Concept wise


π‘‘π‘˜/𝑑π‘₯=0 (𝑑(π‘₯))/𝑑π‘₯=1 (𝑑(π‘˜π‘₯))/𝑑π‘₯=π‘˜ (𝑑(π‘₯^𝑛))/𝑑π‘₯=𝑛π‘₯^(𝑛 βˆ’ 1) (𝑑(𝑒^π‘₯))/𝑑π‘₯=𝑒^π‘₯ (𝑑(ln⁑〖(π‘₯)γ€—))/𝑑π‘₯=1/π‘₯ (𝑑(π‘Ž^π‘₯))/𝑑π‘₯=π‘Ž^π‘₯ γ€– logγ€—β‘π‘Ž (𝑑(π‘₯^π‘₯))/𝑑π‘₯=π‘₯^π‘₯ (1+ln⁑π‘₯) (𝑑(log_π‘Žβ‘π‘₯))/𝑑π‘₯=1/π‘₯Γ—1/lnβ‘π‘Ž (𝑑(sin⁑π‘₯))/𝑑π‘₯=cos⁑π‘₯ (𝑑(cos⁑π‘₯))/𝑑π‘₯=sin⁑π‘₯ (𝑑(tan⁑π‘₯))/𝑑π‘₯=sec^2⁑π‘₯ (𝑑(cot⁑π‘₯))/𝑑π‘₯=βˆ’cosec^2⁑π‘₯ " " (𝑑(sec⁑π‘₯))/𝑑π‘₯=sec⁑π‘₯ tan⁑π‘₯ (𝑑(cosec⁑π‘₯))/𝑑π‘₯=γ€–βˆ’cosec〗⁑π‘₯ cot⁑π‘₯ (𝑑(sin^(βˆ’1)⁑π‘₯))/𝑑π‘₯= 1/√(1 βˆ’ π‘₯^2 ) (𝑑(cos^(βˆ’1)⁑π‘₯))/𝑑π‘₯= (βˆ’1)/√(1 βˆ’ π‘₯^2 ) (𝑑(tan^(βˆ’1)⁑π‘₯))/𝑑π‘₯= 1/(1 + π‘₯^2 ) (𝑑(cot^(βˆ’1)⁑π‘₯))/𝑑π‘₯= (βˆ’1)/(1 +γ€– π‘₯γ€—^2 ) (𝑑(sec^(βˆ’1)⁑π‘₯))/𝑑π‘₯= 1/(|π‘₯| √(π‘₯^2 βˆ’ 1)) (𝑑(cosec^(βˆ’1)⁑π‘₯))/𝑑π‘₯= (βˆ’1)/(π‘₯√(π‘₯^2 βˆ’ 1)) Product Rule 𝑑/𝑑π‘₯(𝑓(π‘₯) 𝑔(π‘₯))=𝑓^β€² (π‘₯) 𝑔(π‘₯)+𝑓(π‘₯) 𝑔^β€² (π‘₯) Quotient Rule 𝑑/𝑑π‘₯ (𝑓(π‘₯)/𝑔(π‘₯) )=(𝑓^β€² (π‘₯) 𝑔(π‘₯) βˆ’ 𝑓(π‘₯) 𝑔^β€² (π‘₯))/(𝑔 (π‘₯))^2 Chain Rule (𝑑(𝑓(𝑔(π‘₯))))/𝑑π‘₯=𝑓^β€² (𝑔(π‘₯)) 𝑔^β€² (π‘₯) First Derivative Rule f’(x) = (π‘™π‘–π‘š)┬(β„Žβ†’0) 𝑓⁑〖(π‘₯ + β„Ž) βˆ’ 𝑓(π‘₯)γ€—/β„Ž

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.