Differential calculus - Table of derivatives

Independent variable : x
Real constants : C,a,b,c
Natural number : n

  1. \({d \over dx}(C)=0\)
  2. \({d \over dx}(x)=1\)
  3. \({d \over dx}(ax+b)=a\)
  4. \({d \over dx}(ax^2+bx+c)=ax+b\)
  5. \({d \over dx}(x^n)=nx^{n-1}\)
  6. \({d \over dx}(x^{-n})=-{n \over x^{n+1} }\)
  7. \({d \over dx} ({1 \over x })= -{1 \over x^2 }\)
  8. \({d \over dx}(\sqrt x)={1 \over 2 \sqrt x }\)
  9. \({d \over dx}(\sqrt [n] x)={1 \over n \sqrt [n] {x^{n-1} }}\)
  10. \({d\over dx} (In\,x)= - {1 \over x}\)
  11. \({d \over dx} (log_ax)= {1 \over x\, In \,a }, a> 0 ,a \neq 1.\)
  12. \({d \over dx } (a^x)= a^xIn\,a\,, a>0, a\neq1.\)
  13. \({d \over dx } (e^x)=e^x\)
  14. \({d \over dx }(sin\,x)= cos \, x\)
  15. \({d \over dx }(cos\,x)= -sin \, x\)
  16. \({d \over dx }(tan\,x)= {1 \over cos^2 x }= sec^2x\)
  17. \({d \over dx }(cot\,x)= -{1 \over sin^2 x }= -csc^2x\)
  18. \({d \over dx }(sec\,x )=tan\,x.sec\,x\)
  19. \({d \over dx }(csc\,x )=-cot\,x.csc\,x\)
  20. \({d \over dx }(arcsin\,x)= {1 \over \sqrt {1-x^2}}\)
  21. \({d \over dx }(arccos\,x)=-{1 \over \sqrt {1-x^2}}\)
  22. \({d \over dx }(arctan\,x)={1 \over 1+x^2}\)
  23. \({d \over dx }(arccot\,x)=-{1 \over 1+x^2}\)
  24. \({d \over dx }(arcsec\,x)= {1 \over |x|\sqrt {x^2-1}}\)
  25. \({d \over dx }(arccsc\,x)= -{1 \over |x|\sqrt {x^2-1}}\)
  26. \({d \over dx} (sinh \, x)=cosh \, x\)
  27. \({d \over dx} (cosh \, x)=sinh \, x\)
  28. \({d \over dx} (tanh \, x)= {1 \over cosh^2x }= sech^2x\)
  29. \({d \over dx} (coth \, x)= -{1 \over sinh^2x }= -csch^2x\)
  30. \({d \over dx} (sech \, x)= -sech \,x. tanh\, x\)
  31. \({d \over dx} (csch \, x)= -csch \,x. coth\, x\)
  32. \({d \over dx } (arcsinh \, x)= {1 \over \sqrt{x^2+1}}\)
  33. \({d \over dx } (arccosh \, x)= {1 \over \sqrt{x^2-1}}\)
  34. \({d \over dx } (arctanh \, x)= {1 \over 1-x^2}, |x| < 1.\)
  35. \({d \over dx } (arccoth \, x)= -{1 \over x^2-1}, |x| >1.\)
  36. \({d \over dx } (u^v)=vu^{v-1}.{du \over dx }+u^vIn\, u.{dv \over dx}\)