Derivation of trigonometric functions

Derivative Calculator

Function of x

First derivative of the function after x

Input field for the function:

f(x)=

clear

Derivative ddxf(x)

next Derivative dndxnf(x)

Plot

Pos1

Ende

7

8

9

/

x

4

5

6

*

(

)

1

2

3

-

a

b

c

0

.

+

sin

cos

tan

ex

ln(x)

xa

^

asin

acos

atan

x2

x

x3

x4

()()

sinh

cosh

asin(bx+c)

acos(bx+c)

atan(bx+c)

1sin(x)

asin2(bx+c)

acos2(bx+c)

atan2(bx+c)

1cos(x)

sin(ax)cos(bx)

exsin(x)cos(x)

sin(cos(x))

1tan(x)

Notations

Notations for derivatives:

d d x f ( x ) = d f d x ( x ) = d f ( x ) d x = f ( x )

Derivation of trigonometric functions

d d x sin(x) = cos(x)

d d x cos(x) = -sin(x)

d d x sin(kx) = kcos(kx)

d d x cos(kx) = -ksin(kx)

d d x tan(x) = d d x sin(x) cos(x) = 1 cos2(x)

d d x cot(x) = - 1 sin2(x)

d d x arcsin(x) = 1 1-x2

d d x arccos(x) = - 1 1-x2

d d x arctan(x) = 1 1+x2

d d x arccot(x) = - 1 1+x2

Derivation rules in short

Factor rule: A constant factor is preserved when differentiate

( af ) = af

Sum rule: When deriving a sum, the summands can be derived individually

( f1 + f2 ) = f1 + f2

Product rule: Rule for deriving products

( uv ) = uv + uv

Quotient rule: Rule for deriving quotients

( u v ) = uv-uv v2

Chain rule: Nested functions go into a product of the inner and outer derivatives when differentiated

( f(g(x)) ) = f(g)g(x)

More Calculators

Here is a list of of further useful calculators:

Index Derivative calculus Partial derivatives and gradient Derivative fraction Derivative roots Derivative e-function Derivative sinh cosh tanh Derivative table Gradient calculator Gradient 2d Plot Function Plot ODE first order