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))
D Dazed New member Joined Jun 15, 2005 Messages 24 Jun 21, 2005 #1 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))
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Jun 21, 2005 #2 Hello, Dazed! These are all applications of the Chain Rule. Find f ' in terms of g' 1. f(x) = g(x<sup>2</sup>) . Click to expand... f '(x) . = . g'(x<sup>2</sup>)·(2x) 2. f(x) = (x<sup>a</sup>) g(x<sup>b</sup>) . Click to expand... 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)) Click to expand... f '(x) . = . cos(g(x))·g'(x)
Hello, Dazed! These are all applications of the Chain Rule. Find f ' in terms of g' 1. f(x) = g(x<sup>2</sup>) . Click to expand... f '(x) . = . g'(x<sup>2</sup>)·(2x) 2. f(x) = (x<sup>a</sup>) g(x<sup>b</sup>) . Click to expand... 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)) Click to expand... f '(x) . = . cos(g(x))·g'(x)
