Page 13 - Math SL HB Sem 2

The chain rule

If g is differentiable at the point x and f is differentiable at the point g(x), then the
composition fo-c is differentiable at the point & moreovsr if
y =f(e@) and u:s(t)
then y=(u) and
dy dy d"
dt du dx

Example:
Iff6l : *n nd g(x) : a2 + Jx then
:
f(g(x) f(x'!+],;r) = -r' + 3:) r

Example :

Differentiate the following

4
a) ' Jt-zx

b) y: G Qx+ 1)3
l+3:r
c) v
-r2 +l
d) y=4tun) ox)
I Itl .){
e)

I
.fi ,t--
^l2e-'+l
_r
;r:In l
E) (;r+2[.r-3)