exists,
then it is denoted by 
and is called the derivative of y with respect to x.|
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rbmix.com |
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Differentiation
Let y = f(x) be a function of x. Let dx be a small change in x and dy the corresponding change in y. That is, y + dy = f(x+dx) . Therefore
dy = f(x+dx) - f(x)
If
exists,
then it is denoted by
and is called the derivative of y with respect to x.
that
is, 
.
some standard formulae are given below
*
*
*
Derivatives of some standard functions
|
y |
|
|---|---|
|
c (constant) |
0 |
|
e x |
e x |
|
x n |
n x n-1 |
|
a x |
a x (ln a ) |
|
sin(x) |
cos(x) |
|
cos(x) |
- sin(x) |
|
tan(x) |
sec2(x) |
|
cot(x) |
-cosec2(x) |
|
sec(x) |
sec(x)tan(x) |
|
cosec(x) |
- cosec(x)cot(x) |
|
sin-1(x) |
|
|
cos-1(x) |
|
|
tan -1(x) |
|
|
sec-1(x) |
|
|
cosec-1(x) |
|
|
cot-1(x) |
|
|
uv |
uv' + vu' (product rule) |
|
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