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Tangent Line Calculator

The calculator will find the tangent line to the explicit, polar, parametric and implicit curve at the given point, with steps shown.

It can handle horizontal and vertical tangent lines as well.

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:
TypeGet
Constants
ee
pi`pi`
ii (imaginary unit)
Operations
a+ba+b
a-ba-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)`
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)

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`x_0=`( )

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