2 | Inverse Functions
Procedure Exercises
1 Find f 0 in terms of g 0 given that f (x) = g(ln x).
2 Dierentiate
g(t) =
et
.
1 − et
3 Find f (n) if ln(2x).
4 Find the derivative of the function. Find the domains of the function and its
derivative.
f (x) = arcsin(ex ).
5 Find y 0 if tan−1 (x2 y) = x + xy 2 .
Principle Exercises
6 Prove that
1
d
(sec−1 x) = √
dx
x x2 − 1
7 Find the limit:
lim arccos
x→∞
1 + x2
1 + 2x2
8 Prove the identity:
arcsin
√
x−1
π
= 2 arctan x −
x+1
2
Whats next?
Remember to work on the hypobolic functions worksheet on SunLearn.
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