Online Derivative Calculator with Steps
The online calculator will calculate the derivative of any function using the common rules of differentiation (product rule, quotient rule, chain rule, etc.), with steps shown. It can handle polynomial, rational, irrational, exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic and inverse hyperbolic functions. 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.
Related calculator: Implicit Differentiation Calculator with Steps
- 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.
| 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) |
Your Input
Find .
Solution
Apply the product rule with and :
Apply the power rule with , in other words, :
The derivative of the sine is :
Thus, .