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Calculus: Differentiation and Integration, 1st Edition
book

Calculus: Differentiation and Integration, 1st Edition

by ICFAI
April 2024
Intermediate to advanced content levelIntermediate to advanced
710 pages
20h 50m
English
Pearson India
Content preview from Calculus: Differentiation and Integration, 1st Edition
4-36  Calculus – Differentiation and Integration
=
+
=
+
=
sin( ) sin
sin( ) sin
lim
si
y y y
x
y y y
y
y
x
y
d
d
d
d
d
d
d 0
nn( ) sin
lim
lim
cos sin
y y y
y
y
x
y y
y
y
+
=
+
d
d
d
d
d
d
d
0
0
2
1
2
1
22
1
2
0
d
d
d
d
y
y
dy
dx
y y
y
= +
lim cos

=
sin
( / )
lim c
1
2
2
0
d
d
d
y
y
dy
dx
y
oos lim
sin
( / )
y y
y
y
y
+
1
2
1
2
2
0
d
d
d
d

=
[ ]
dy
dx
y
dy
dx
cos 1
= =
=
dy
dx y
y
x
1 1
1
1
1
2
2
cos
sin
.
Similarly, we can prove that
dy
dx
x
=
1
1
2
for y = cos
-1
x.
2. Find
dy
dx
for the equation y = tan
-1
x.
Given y x
y x
=
=
tan
tan tan(tan )
1
1
=
tan .y x
(1)
Differentiation 4-37
Using implicit differentiation and solving ...
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Publisher Resources

ISBN: 9789353948221