## Blog 96

Dear Students,We know that, everyone of us have list of formulae of so many mathematical theory from so many sources. This blog will give you the derivative integration calculator, which display the derivative and integration of the function which you choose from the drop down menu of the calculator.

#### Click on the following button:

The list of all the functions and their derivative and integration is give below.

f(x) | Derivative | Integration |

a | 0 | ax + c |

x | 1 | x ^{2}/2 + c |

1/x | [-1/(x ^{2})] | ln|x| + c |

x ^{n} | nx ^{(n-1)} | [(x ^{(n+1)})/(n+1)]+c n#(-1) |

ln|x| | 1/x | (x ln|x|) - x + c |

a ^{x} | a ^{x} (ln|a|) | a ^{x}/ln(|a|) |

e ^{x} | e ^{x} | e ^{x }+ c |

sin x | cos x | (-cos x) + c |

cos x | (-sin x) | sin x + c |

tan x | sec ^{2} x | ln|(sec x)| + c |

csc x | (-csc x) cot x | [-ln|csc x + cot x|] + c |

sec x | sec x tan x | ln|sec x + tan x| + c |

cot x | (-csc ^{2} x) | ln|sin x| + c |

arcsin x | 1/√[1-x ^{2}] | x arcsin x + √[1-x ^{2}] + c |

arccos x | {-1/√[1-x ^{2}] | x arccos x - √[1-x ^{2}] + c |

arctan x | 1/[1+(x ^{2})] | x arctan x - [1/2(ln|1+x ^{2}|] + c |

arccsc x | {-1/|x|√[(x ^{2})-1]} | x arccsc x + |x|√ [x+(x ^{2})-1] + c |

arcsec x | {1/|x|√[(x ^{2})-1]} | x arcsec x - arctanh x √[1-(1/x ^{2})] + c |

arccot x | [-1/(1+x ^{2})] | x arccot x + [ln|(1+x ^{2})/2] + c |

sinh x | cosh x or [(e ^{x}) + (e^{-x})]/2 | cosh x + c |

cosh x | sinh x or [(e ^{x}) - (e^{-x})]/2 | sinh x + c |

tanh x | sech ^{2} x | ln|cosh x| +c |

csch x | [-coth x csch x] | ln|tanh (x/2)| + c |

sech x | [-tanh x sech x] | arctan (sinh x) + c |

coth x | [-csch x] | ln|sinh x| + c |

Dear students,

you are always welcome to suggest us your valuable opinions. The calculator will be improved with more functions as per your requirement.

Your valuable comments will improve our blog and always will motivate us to write more and more basics of Mathematics.