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 Formulas - Part 2

Differentiation of Trigonometry Functions

Differentiation Formulas - Part 3

Differentiation of Inverse Trigonometry Functions

Differentiation Formulas - Part 4

Differentiation Rules

Differentiation Formulas - Part 5


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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.