Field is empty
'%1' is not a valid email address.
Field must not be empty.
It must be at least %1 characters long.
It must be less than %1 characters long.
It must be the same as the field '%1' value.
Invalid symbol entered. Allowed symbols:'%1'.
Number expected.
Positive number expected.
Integer expected.
Positive integer expected.
Values must be in the range [%1 .. %2].
Symbol %1 is already entered in allowed character set.
Field value must be less than %1.
First character must be a Latin letter.
Sun
Mon
Tue
Wed
Thu
Fri
Sat
January
February
March
April
May
June
July
August
September
October
November
December
century
B.C.
%1 century
Error occurred while importing data on line:%1. Invalid value: '%2'. Error: %3
"Could not determine a data field separator. You may use one of the following characters to separate data fields: tab, ';' or ','."
%2/%3/%1%4
%2/%3/%1%4 %6:%7
N
S
E
W
yes
no
Invalid file format. We support only the following formats: %1
Please leave your email or phone number.
minutes
minutes
minute
minutes
minutes
minutes
minutes
minutes
minutes
minutes
minutes
minutes
minutes
hour
hours
hours
hours
hours
hours
hours
hours
hours
hours
hours
days
day
days
days
days
days
days
days
days
days
days
days
month
months
months
months
months
months
months
months
months
months
months
year
years
years
years
years
years
years
years
years
years
years
ago
%1 minutes ago
%1 minutes ago
%1 minute ago
%1 minutes ago
%1 minutes ago
%1 minutes ago
%1 minutes ago
%1 minutes ago
%1 minutes ago
%1 minutes ago
%1 minutes ago
%1 minutes ago
%1 minutes ago
%1 hour ago
%1 hours ago
%1 hours ago
%1 hours ago
%1 hours ago
%1 hours ago
%1 hours ago
%1 hours ago
%1 hours ago
%1 hours ago
%1 hours ago
%1 days ago
%1 day ago
%1 days ago
%1 days ago
%1 days ago
%1 days ago
%1 days ago
%1 days ago
%1 days ago
%1 days ago
%1 days ago
%1 days ago
%1 month ago
%1 months ago
%1 months ago
%1 months ago
%1 months ago
%1 months ago
%1 months ago
%1 months ago
%1 months ago
%1 months ago
%1 months ago
%1 year ago
%1 years ago
%1 years ago
%1 years ago
%1 years ago
%1 years ago
%1 years ago
%1 years ago
%1 years ago
%1 years ago
%1 years ago
HTML code for site/blog
Appearance
Sample
Close
Sofia Vasilievna
ProfessionalEngineering

Derivative calculator

Online calculator which determines first derivative of a function
Anton2010-01-24 17:05:55
This calculator finds derivative of entered function and tries to simplify the formula.

Use "Function" field to enter mathematical expression with x variable. You can use operations like addition +, subtraction -, division /, multiplication *, power ^, and common mathematical functions. Full syntax description can be found below the calculator.

Simplification of derivative formula can take great amount of time, especially for complex expressions. You can use "Stop" button to stop simplification and see current results. Usually 10-15 seconds yield good enough result.

Derivative calculatorCreative Commons Attribution/Share-Alike License 3.0 (Unported)
Function derivative:

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

Finding derivative



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.

Differentiation rules



1) the sum rule:
(u+v+...+w)'=u'+v'+...+w'
2) the product rule:
(uv)'=u'v+v'u
3) the quotient rule:
(\frac{u}{v})'=\frac{u'v-v'u}{v^2}
4) the chain rule:
y=f(u), u=\phi(x), y'=f'(u)\phi'(x)

Derivatives of common functions



The polynomial or elementary power:
(x^{n})'=nx^{n-1}
The exponential function:
(a^{x})'=a^{x}\ln(a)
(e^{x})'=e^{x}
The logarithmic function:
(\ln(x))'=\frac{1}{x}
The trigonometric functions:
(\sin{x})'=\cos{x},
(\cos(x))'=-\sin(x),
(\tan(x))'=\frac{1}{\cos^2(x)},
(\cot(x))'=-\frac{1}{\sin^2(x)}
The inverse trigonometric functions:
(\arcsin(x))'=\frac{1}{\sqrt{1-x^2}},
(\arccos(x))'=-\frac{1}{\sqrt{1-x^2}},
(arctg(x))'=\frac{1}{1+x^2},
(arcctg(x))'=-\frac{1}{1+x^2}
The hyperbolic functions:
(sh(x))' = ch(x)
(ch(x))' = sh(x)
(th(x))' = -th(x)sech(x)
(cth(x))' = -csch^2(x)


Not suitable?

View all calculators
(228 calculators in total. )
Request a calculator
 

Comments

Spam filter
Send comment