Q.1
Differentiate sin(√sinx + cosx)
Solution
Q2
Differentiate cos (x3) sin2 (x5)
Solution
Q3
If y = 
cosx + sinx
/
cosx - sinx
, prove that
dy
/
dx
= sec2 (
π
/
4
+ x)
Solution
Q4
Differentiate √(
1 - tanx
/
1 + tanx
)
Solution
Q5
If f(x) = |cos x - sin x|, find f'(
π
/
6
).
Solution
Q6
If f(x) = √x2 + 1 ; g(x) = 
x + 1
/
x2 + 1
and h(x) = 2x - 3, then find f'[h'{g'(x)}].
Solution
Q7
Prove that 
d
/
dx
(
x
/
2
√a2 - x2 +
a2
/
2
sin-1
x
/
a
) = √a2 - x2
Solution
Q8
Differentiate cos-1(sinx)
Solution
Q9
Differentiate tan-1(√
1 - cosx
/
1 + cosx
)
Solution
Q10
Find 
dy
/
dx
when y = sin-1 (
3 sinx + 4 cosx
/
5
)
Solution
Q11
Find 
dy
/
dx
when y = sin-1(
√1 + x - √1 - x
/
2
)
Solution
Q12
If y = sec-1(
√x + 1
/
√x - 1
) + sin-1(
√x - 1
/
√x + 1
), prove that
dy
/
dx
is independent of x
Solution
Q13
If y = tan-1
5ax
/
a2 - 6x2
prove that
dy
/
dx
=
3a
/
a2 + 9x2
+
2a
/
a2 + 4x2
Solution