Online Derivative Calculator with Steps

The online calculator will calculate the derivative of any function, with steps shown. Also, it will evaluate the derivative at the given point, if needed. It also supports computing the first, second and third derivatives, up to 10.

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)

Enter a function:

How many times to differentiate?

Variable:

Evaluate the derivative at the point

Leave empty, if you don't need derivative at the specific point

Write all suggestions in comments below.

Solution

Your input: find $$$\left(x \sin{\left (x \right )}\right)^{\prime }$$$.

Apply the product rule $$$\left(f\left(x\right)\cdot g\left(x\right)\right)^{\prime }=\left(f\left(x\right)\right)^{\prime } \cdot g\left(x\right) + f\left(x\right) \cdot \left(g\left(x\right)\right)^{\prime }$$$ with $$$f\left(x\right)=x$$$ and $$$g\left(x\right)=\sin{\left (x \right )}$$$:

Apply the power rule $$$\left(x^{n}\right)^{\prime }=n\cdot x^{-1+n}$$$ with $$$n=1$$$, in other words $$$\left(x\right)^{\prime }=1$$$:

Derivative of sine is $$$\left(\sin{\left (x \right )}\right)^{\prime }=\cos{\left (x \right )}$$$:

Thus, $$$\left(x \sin{\left (x \right )}\right)^{\prime }=x \cos{\left (x \right )} + \sin{\left (x \right )}$$$.

Answer: $$$\left(x \sin{\left (x \right )}\right)^{\prime }=x \cos{\left (x \right )} + \sin{\left (x \right )}$$$