Page 15 - Math SL HB Sem 2

Example 1l:

:2.
Find the slope of the tangent to x2 + y3 5 at the point where x
=
Hence, find the equation ofthe tangent.

Higher derivatives

If the derivative f' of a function f is itself differentiable, then the derivative of f is
denoted by /'and is called the second derivative of f. As long as. we have

differentiability we can continue the process of differentiating derivatives to obtain
third, fourth fifth and even higher derivatives of f denoted by

r=u.l = 41
ctr'
I = rrt= *
dx

f : d'y
dx'

In general we write
,

y'")6) a Lr(x)l
dt'