,
(sin )
dy
d
y
dx
+dx
 =
d(cos )
x
dx
which implies using chain rule
cos
dy
ydy
dx
dx
+
⋅
 = – sin x
This gives
dy
dx  =
sin
1
cos
x
y
− +
where
y ≠ (2n + 1) π
Rationalised 2023-24
 MATHEMATICS
124
5 3 3  Derivatives of inverse trigonometric functions
We remark that inverse trigonometric functions are continuous functions, but we will
not prove this Now we use chain rule to find derivatives of these functions