Differentiation
Exercises for students
Differentiate the following with respect to x and check your working using the above applet:
| y = 3x^2 sin (5x)
| y = x^2 exp(-3x)
| y = ln(x) / x^2
| y = exp(3x) / x
|
| y = (3 - 4x^2)1/2
| y = ( sin x )2
| y = sin ( x^3 + 4 )
| y = ln (1 + sin x)
|
Summary
| Product Rule: | d | (uv) = u | dv | + v | du |
| Quotient Rule: | d | u | = | v du - u dv |
| dx | dx | dx |
dx | v | v2 |
| d | (f(x))n = | n (f(x))n-1 f'(x) |
| dx |
| d | sin x = | cos x | |
d | cos x = | - sin x | |
d | tan x = | sec2 x |
| dx | dx | dx |
| d | ex = | ex | |
d | ln x = | 1 / x | |
d | ax = | ax ln a |
| dx | dx | dx |
| d | sec x = | sec x tan x | |
d | cot x = | - cosec2 x | |
d | cosec x = | - cosec x cot x |
| dx | dx | dx |
| d | sin-1 x = | 1 | |
d | cos-1 x = | - 1 | |
d | tan-1 x = | 1 |
| dx | sqrt(1 - x2) |
dx | sqrt(1 - x2) |
dx | 1 + x2 |
You can define the function using the following operators:
| + | - | * | / | ^ |
| sqrt( ) | ln( ) | exp( ) | pi |
| sin( ) | cos( ) | tan( ) |
| asin( ) | acos( ) | atan( ) |
| sinh( ) | cosh( ) | tanh( ) |
Right click here to download a summary of the topic of Differentiation.
Right-click here to download this page, the Java Class File and unzip the Javathings Math Package.
Back to H2 Mathematics Homepage
This applet uses the com.javathings.math package developed by:
Patrik Lundin
patrik@javathings.com
http://www.javathings.com