This calculator finds the derivative of an entered function and tries to simplify the formula.
Use the "Function" field to enter a mathematical expression with x variable. You can use operations like addition +, subtraction -, division /, multiplication *, power ^, and common mathematical functions. You can find the full syntax description below the calculator.
Simplification of derivative formula can take a great amount of time, especially for complex expressions. You can use the "Stop" button to stop simplification and see current results. Usually, 10-15 seconds yield a good enough result.
Function formula syntax
In function notation you can use one variable (always use x), brackets, pi number (pi), exponent (e), operations: addition +, subtraction -, division /, multiplication *, power ^.
You can use following common functions: sqrt - square root,exp - power of exponent,lb - logarithm to base 2,lg - logarithm to base 10,ln - logarithm to base e,sin - sine,cos - cosine,tg - tangent,ctg - cotangent,sec - secant,cosec - cosecant,arcsin - arcsine,arccos - arccosine,arctg - arctangent,arcctg - arccotangent,arcsec - arcsecant,arccosec - arccosecant,versin - versien,vercos - vercosine,haversin - haversine,exsec - exsecant,excsc - excosecant,sh - hyperbolic sine,ch - hyperbolic cosine,th - hyperbolic tangent,cth - hyperbolic cotangent,sech - hyperbolic secant,csch - hyperbolic cosecant, abs - module, sgn - signum (sign), logP - logarithm to base P, f.e. log7(x) - logarithm to base 7, _rootP - P-th root, f.e. root3(x) - cubic root
To get derivative is easy using differentiation rules and derivatives of elementary functions table. The challenging task is to interpret entered expression and simplify the obtained derivative formula. I do my best to solve it, but it's another story.
1) the sum rule:
2) the product rule:
3) the quotient rule:
4) the chain rule:
Derivatives of common functions
The polynomial or elementary power:
The exponential function:
The logarithmic function:
The trigonometric functions:
The inverse trigonometric functions:
The hyperbolic functions: