Differentiation Formulas

This list consists of all the differentiation formulas. This includes differentiation formula for trigonometric, polynomial, hyperbolic, logarithmic, exponential, rational, inverse trigonometric functions etc.

Differentiation - Formulas

In all the formulas below, f’ means \( \frac{d(f(x))}{dx} = f'(x)\) and g’ means \(\frac{d(g(x))}{dx}\) = \(g'(x)\) . Both f and are the functions of x and differentiated with respect to x.

  1. Power Rule: \(\frac{d(f(x))}{dx}(x^n)\) = \(nx^{n-1}\)
  2. Derivative of a constant, a: \(\frac{da}{dx}\) = \(0\)
  3. Derivative of a constant multiplied with function \(f: \frac{d}{dx}a . f \)=\( af'\)
  4.  Sum Rule: \(\frac{d}{dx}(f \pm g)\) = \(f’ \pm g'\)

5. Product Rule: \( \frac{d}{dx}(fg)\) = \(fg’ + gf’ \)

6. Quotient Rule:\(\frac{d}{dx}(\frac{f}{g})\) = \(\frac{gf’ – fg’}{g^2}\)

7. \(\frac{d}{dx} (sin~ x)\) = \(cos~ x\)

8. \(\frac{d}{dx} (cos~ x)\) = \(- sin~ x\)

9. \(\frac{d}{dx} (tan ~x)\) =\( sec^2 ~x\)

10. \(\frac{d}{dx} (cot~ x)\) = \(-csc^2~ x\)

11. \(\frac{d}{dx} (sec~ x)\) =\( sec~ x~ tan ~x\)

12.  \(\frac{d}{dx} (csc ~x)\) = \(-csc~ x cot~ x\)

13. \(\frac{d}{dx} (sinh~ x)\) = \(cosh~ x\)

14. \(\frac{d}{dx} (cosh~ x)\) = \(sinh~ x\)

15. \(\frac{d}{dx} (tanh ~x)\)= \(sech^2~ x\)

16. \(\frac{d}{dx} (coth~ x)\) =\( -csch^2~ x\)

17. \(\frac{d}{dx} (sech~ x)\) = \(-sech ~x~ tanh ~x\)

18. \(\frac{d}{dx} (csch~ x )\) = \(-csch~ x~ coth ~x\)

19. \(\frac{d}{dx}(sin^{-1}~ x)\) = \(\frac{1}{\sqrt{1 – x^2}}\)

20. \(\frac{d}{dx}(cos^{-1}~ x)\) = \(-\frac{1}{\sqrt{1 – x^2}}\)

21. \(\frac{d}{dx}(tan^{-1}~ x)\) = \(\frac{1}{1 + x^2}\)

22. \(\frac{d}{dx}(cot^{-1}~ x)\) = \(-\frac{1}{1 + x^2}\)

23. \(\frac{d}{dx}(sec^{-1} ~x) \)= \(\frac{1}{|x|\sqrt{x^2 – 1}}\)

24. \(\frac{d}{dx}(csc^{-1}~x) \)= \(-\frac{1}{|x|\sqrt{x^2 – 1}}\)

25. \(\frac{d}{dx}(a^x) \)= \(a^x ln a\)

26. \(\frac{d}{dx}(e^x) \)= \(e^x\)

27. \(\frac{d}{dx}(log_a~ x)\) = \(\frac{1}{(ln~ a)x}\)

28. \(\frac{d}{dx}(ln~ x)\) = \(\frac{1}{x}\)

29. Chain Rule: \(\frac{dy}{dx}\) = \(\frac{dy}{du} × \frac{du}{dx}\) = \(\frac{dy}{dv} × \frac{dv}{du} × \frac{du}{dx}\)<

Bookmark this page and visit whenever you need a sneak peek at differentiation formulas. Visit this page for integration formulas. To have a cheat sheet of all the formulas from different chapters, search them at byjus.com.


Practise This Question

In which of the following quadrilaterals, a diagonal is not an angle bisector?