# 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.

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?