Find f' in terms of g'

Dazed

New member
Joined
Jun 15, 2005
Messages
24
Find f' in terms of g'

1. f(x) = g(x^2)

2. f(x) = (x^a)g (x^b)

3. f(x) = sin (g(x))
 

soroban

Elite Member
Joined
Jan 28, 2005
Messages
5,588
Hello, Dazed!

These are all applications of the Chain Rule.

Find f ' in terms of g'

1. f(x) = g(x<sup>2</sup>)
.
f '(x) . = . g'(x<sup>2</sup>)·(2x)


2. f(x) = (x<sup>a</sup>) g(x<sup>b</sup>)
.
We need the Product Rule, too.

f '(x) . = . x<sup>a</sup>·g'(x<sup>b</sup>)·(bx<sup>b-1</sup>) + ax<sup>a-1</sup>·g(x<sup>b</sup>)


3. f(x) = sin(g(x))
f '(x) . = . cos(g(x))·g'(x)
 
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