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INTRODUCTION
5) 
Proof:
Let f(x) = sinx then,
Hence,
6) 
7) 
8) 
9) 
10)  Why?
Proof:
Let f(x) = secx
Hence,
11) 
Proof:
Let  then x = siny.
Differentiating w.r.t x we get,
Hence,
12) 
13) 
14) 
15) 
16)  Why?
Proof:
Let y = sec-1x then secy = x.
Differentiating w.r.t x we have,
Hence,
Dumb Question:
Why and not  ?
Ans:
Fig (4)
Note that y = sec-1x is an increasing function in its domain.
So,
Illustration 6:
Differentiate 
Solution:
Different Methods of Differentiation:
1) Differentiation of a function defined parametrically:
Let x, y be function of parameter t, i.e.
x = f (t), y = f (t) then,
Illustration:
Solution:
2) Logarithmic Differentiation:
The process of taking logarithm on both sides and then differentiating is called logarithmic differentiation.
Illustration 8:
Differentiate  w.r.t x.
Solution:
Let y = .
Taking logarithm on both sides, then we have
logy = sinx.logx
3) Differentiation of Implicit function:
If the relation between x and y is given by equation containing both and this equation is not immediately solvable for y, then y is called implicit function of x.
Illustration 9:
If  Then prove that 
Solution:
Given that differentiating on both sides w.r.t x we have,
Hence,
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Vriti Edustore
