Pimpri-Chinchwad Education and Socio-Economic Trust’s
Derivative
1.
=0
2.
=1
3.
=n
4.
=
5.
=
6.
=
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19. Chain Rule For Composite Functions:If y = f(u) and u = g(x) are two
functions, then y = f[g(x)] is a composite function. In this case
=
*
20. Inverse Functions : If y = f(x) and x = g(y) where g is inverse function of
y.Then
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Pimpri-Chinchwad Education and Socio-Economic Trust’s
21.Parametric Functions : Two variables x and y when expressed as functions of
the same variable t i.e. x = f(t) and y = g(t) where t is called a parameter then
≠0
where
Integration
Definition:- If f(x) and g(x) are two functions such that
= g(x), then f(x) is
called an Integral or an antiderivative or a primitive of g(x) with respect to x and
is denoted as
x = f(x) .
Rules of Integration:
1.
x) + g(x) ]dx =
dx +
2.
x) - g(x) ]dx =
dx -
3.
4.
x)]dx =
If
dx
dx
dx where k is constant
= g(x) + c .then
= g(ax+b) + c a ≠ 0.
Standard Integrals :
1.
2.
=
3.
= log(x) + c
4.
- cosx + c
5.
dx = sinx + c
6.
+c
= log ( secx ) + c
7.
cotx dx
= log ( sinx ) + c
8.
secx dx
= log ( secx + tanx ) + c = log | tan( +
)| + c
9.
dx = log | cosecx- cotx| + c = log |tan( )| + c
10.
dx = tanx + c
11.
x dx = -cotx +c
12.
secx.tanx dx = secx + c
13.
cosecx.cotx dx = -cosecx + c
14.
dx
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=
+c
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Pimpri-Chinchwad Education and Socio-Economic Trust’s
15.
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dx
=
+c
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