Online Derivative Calculator with Steps

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

Show Instructions
  • In general, you can skip 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 multiplication sign, type at least 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 table below you can notice, that sech is not supported, but you can still enter it using 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 welcomed. Leave them in comments
The following table contains 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 function:

How many times to differentiate?

Variable:

Evaluate derivative at point

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

Write all suggestions in comments below.

Solution

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

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