Differentiation and Integration are two parts of the calculus. We need to do learn some basic formulas of differentiation and integration. Here we are mentioning some major formulas. And others are in the attached PDF.
Differentiation is just finding the slope. It is a process where one finds the instantaneous rate of change in function based on one of its variables. And integration is the reverse process of differential calculation. It is a mathematical process where one tries to find a function with its derivative.
Some basic differential and integral formulas are mentioned below. Besides, a lot more formulas have been given in the PDF. The attached PDF file has a total of 32 differential formulas along with limits. And it also contains 36 integral formulas. PDF has been previously published on ‘Pathgriho The Reading Room’. And yeah, this PDF is handwritten, not a typed one.
Some Differential Formulas
- `\(\frac{d}{dx} (cos~x)= – sin\ x\)`
- `\(\frac{d}{dx} (tan x)= sec^{2} x\)`
- `\(\frac{d}{dx} (cotx = -cosec^{2} x\)`
- `\(\frac{d}{dx} (sec x) = sec\ x\ tan\ x\)`
- `\(\frac{d}{dx} (cosecx)= -cosec\ x\ cot\ x\)`
- `\(\frac{d}{dx} (sinhx)= cosh\ x\)`
- `\(\frac{d}{dx} (coshx) = sinh\ x\)`
- `\(\frac{d}{dx} (tanhx)= sech^{2} x\)`
- `\(\frac{d}{dx} (cothx)=-cosech^{2} x\)`
- `\(\frac{d}{dx} (sechx)= -sech\ x\ tanh\ x\)`
- `\(\frac{d}{dx} (cosechx ) = -cosech\ x\ coth\ x\)`
- `\(\frac{d}{dx} (sinx)= cos\ x\)`
Some Integral Formulas
- ∫ a dx = ax+ C
- ∫ x^{n }dx = ((x^{n+1})/(n+1))+C ; n≠1
- ∫ sin x dx = – cos x + C
- ∫ cos x dx = sin x + C
- ∫ sec^{2}x dx = tan x + C
- ∫ csc^{2}x dx = -cot x + C
- ∫ sec x (tan x) dx = sec x + C
Details about the attached PDF
- It has a total page of 7.
- It contains 32 Differential Formulas
- It contains 36 Integral Formulas
- Size is less than 2 MB
- Uploaded to Google Drive
- Previously published on Pathgriho The Reading Room
FAQs
1. What is Differentiation?
Ans: Differentiation is just finding the slope. It is a process where one finds the instantaneous rate of change in function based on one of its variables.
2. What is Integration?
Ans: Integration is the reverse process of differential calculation. It is a mathematical process where one tries to find a function with its derivative.