# Function Calculator

The calculator will find the domain, range, x-intercepts, y-intercepts, derivative, integral, asymptotes, intervals of increase and decrease, critical points, extrema (minimum and maximum, local, absolute, and global) points, intervals of concavity, inflection points, limit, Taylor polynomial, and graph of the single variable function. The interval can be specified. Parity will also be determined.

Show Instructions

- In general, you can skip the multiplication sign, so `5x` is equivalent to `5*x`.
- In general, you can skip parentheses, but be very careful: e^3x is `e^3x`, and e^(3x) is `e^(3x)`.
- Also, be careful when you write fractions: 1/x^2 ln(x) is `1/x^2 ln(x)`, and 1/(x^2 ln(x)) is `1/(x^2 ln(x))`.
- If you skip parentheses or a multiplication sign, type at least a whitespace, i.e. write sin x (or even better sin(x)) instead of sinx.
- Sometimes I see expressions like tan^2xsec^3x: this will be parsed as `tan^(2*3)(x sec(x))`. To get `tan^2(x)sec^3(x)`, use parentheses: tan^2(x)sec^3(x).
- Similarly, tanxsec^3x will be parsed as `tan(xsec^3(x))`. To get `tan(x)sec^3(x)`, use parentheses: tan(x)sec^3(x).
- From the table below, you can notice that sech is not supported, but you can still enter it using the identity `sech(x)=1/cosh(x)`.
- If you get an error, double-check your expression, add parentheses and multiplication signs where needed, and consult the table below.
- All suggestions and improvements are welcome. Please leave them in comments.

The following table contains the supported operations and functions:

Type | Get |

Constants | |

e | e |

pi | `pi` |

i | i (imaginary unit) |

Operations | |

a+b | a+b |

a-b | a-b |

a*b | `a*b` |

a^b, a**b | `a^b` |

sqrt(x), x^(1/2) | `sqrt(x)` |

cbrt(x), x^(1/3) | `root(3)(x)` |

root(x,n), x^(1/n) | `root(n)(x)` |

x^(a/b) | `x^(a/b)` |

x^a^b | `x^(a^b)` |

abs(x) | `|x|` |

Functions | |

e^x | `e^x` |

ln(x), log(x) | ln(x) |

ln(x)/ln(a) | `log_a(x)` |

Trigonometric Functions | |

sin(x) | sin(x) |

cos(x) | cos(x) |

tan(x) | tan(x), tg(x) |

cot(x) | cot(x), ctg(x) |

sec(x) | sec(x) |

csc(x) | csc(x), cosec(x) |

Inverse Trigonometric Functions | |

asin(x), arcsin(x), sin^-1(x) | asin(x) |

acos(x), arccos(x), cos^-1(x) | acos(x) |

atan(x), arctan(x), tan^-1(x) | atan(x) |

acot(x), arccot(x), cot^-1(x) | acot(x) |

asec(x), arcsec(x), sec^-1(x) | asec(x) |

acsc(x), arccsc(x), csc^-1(x) | acsc(x) |

Hyperbolic Functions | |

sinh(x) | sinh(x) |

cosh(x) | cosh(x) |

tanh(x) | tanh(x) |

coth(x) | coth(x) |

1/cosh(x) | sech(x) |

1/sinh(x) | csch(x) |

Inverse Hyperbolic Functions | |

asinh(x), arcsinh(x), sinh^-1(x) | asinh(x) |

acosh(x), arccosh(x), cosh^-1(x) | acosh(x) |

atanh(x), arctanh(x), tanh^-1(x) | atanh(x) |

acoth(x), arccoth(x), cot^-1(x) | acoth(x) |

acosh(1/x) | asech(x) |

asinh(1/x) | acsch(x) |

If you like the website, please share it anonymously with your friend or teacher by entering his/her email: