Gradient of a Function Calculator

The calculator will find the gradient of the given function (at the given point if needed), with steps shown.

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)`
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)

Enter a function:

Enter the order of variables and/or a point:

If you don't need the order of variables, leave it empty.

If you want a specific order of variables, enter variables comma-separated, like `x,y,z`.

If you want the gradient at a specific point, for example, at `(1, 2, 3)`, enter it as `x,y,z=1,2,3`, or simply `1,2,3` if you want the order of variables to be detected automatically.

If the calculator did not compute something or you have identified an error, please write it in comments below.

Write all suggestions in comments below.

Show steps

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