math handout

1. Section 3.6 Implicit differentiation
Learning outcomes
After completing this section, you will inshaAllah be able to
1. find derivatives of functions defined implicitly
2. find derivatives of expressions involving inverse trigonometric functions
13.6

2. How to perform implicit differentiation?
• We learn implicit differentiation with the help of examples.
Differentiation formulas for inverse trigonometric functions
End of 3.6
23.6
See examples 1, 2, 3, 4, 5, 6, 7, 8 done in class
Recall:
What are implicitly defined functions?
• See class explanation
See example 8 to
understand meaning of
orthogonal curves
• 1
2
1
(sin )
1
u
u
d d
x xud d
−
= ⋅
−
• 1
2
1
(cos )
1
u
u
d d
d dxux
−
= − ⋅
−
• 1
2
1
(tan )
1
u
u
d d
x xud d
−
= ⋅
+
• 1
2
1
(cot )
1
u
u
d d
d dxux
−
= − ⋅
+
• 1
2
1
(sec )
1
u
u
u u
d d
dx dx
−
= ⋅
−
• 1
2
1
(csc )
1
u
u
u
d d
d ux dx
−
= − ⋅
−
See examples 9, 10, 11 done in class