The derivative calculator calculates the derivative or partial derivative of a function f. Additional the calculator computes the gradient in 3d.
Input field for the function to be derived. With 'ok' the entered function is accepted. With ∂/∂... the corresponding derivatives can be formed. Multiple application leads in each case to the derivative of the predecessor function.
f(...) =
Function | Description |
---|---|
sin(x) | Sine of x |
cos(x) | Cosine of x |
tan(x) | Tangent of x |
asin(x) | arcsine |
acos(x) | arccosine of x |
atan(x) | arctangent of x |
atan2(y, x) | Returns the arctangent of the quotient of its arguments. |
cosh(x) | Hyperbolic cosine of x |
sinh(x) | Hyperbolic sine of x |
pow(a, b) | Power ab |
sqrt(x) | Square root of x |
exp(x) | e-function |
log(x), ln(x) | Natural logarithm |
log(x, b) | Logarithm to base b |
log2(x), lb(x) | Logarithm to base 2 |
log10(x), ld(x) | Logarithm to base 10 |
Factor rule: A constant factor is preserved when differentiate
Sum rule: When deriving a sum, the summands can be derived individually
Product rule: Rule for deriving products
Quotient rule: Rule for deriving quotients
Chain rule: Nested functions go into a product of the inner and outer derivatives when differentiated
Basic derivatives:
Derivative n-th root:
Derivation square root:
Derivation cube root:
Derivation of trigonometric functions:
Derivations of the e-function:
Derivation of the logarithm functions:
For functions with more than one variables the derivative to one of the variables is called partial derivative.
For a function with the variable x and several further variables the partial derivative to x is noted as follows.
For partial derivation, the other variables are treated as constants.
Here is a list of of further useful calculators:
Index Derivative calculus Derivative fraction Derivative roots Derivative e-function Derivative sine cosine tangent Derivative sinh cosh tanh Derivative table Gradient calculator Gradient 2d Plot Function Plot ODE first order