[sin(x)] = cos(x) [cos(x)]

d
dx [sin(x)]
= cos(x)
d
dx [tan(x)]
= sec2 (x)
d
−1
(sin
x)
dx
=
√ 1
1−x2
d
−1
x)
dx (tan
=
1
1+x2
Ex:
d
−1
−1 3
(tan
(x )))
(cos
dx
Ex:
d
dx (ln(x))
=
d
dx [cos(x)]
= −sin(x)
d
−1
(cos
x)
dx
=
√ −1
1−x2
Suppose s(t) = t2 + 3t − 1 represents position at time t.
Then velocity = v(t) =
d
dt (s(t))
and acceleration = a(t) =
= s0 (t) =
d
dt (v(t))
= v 0 (t) = s00 (t) =
jerk = change in acceleration
d
= D(a(t)) = dt
(a(t)) = a0 (t) = v 00 (t) = s000 (t) =
Ex: Find
d50
dx50 (sin(x))
=
Ex: Find y 00 if 2x2 y − 3y 2 = 4