If #g(0) = 0#, #f'(0) = 2#, #f(0) = 4# and #g'(0) = 3#, then what is the value of #(f @ g)'(0)#?

1 Answer
Noah G
Dec 4, 2016

#6#.

Explanation:

#(f @ g)(x)# can be written as #f(g(x))#.

The chain rule for derivatives deals with composite functions.

It states that for #f(g(x))#, #dy/dx = f'(g(x))g'(x)#

We now insert our given values inside the derivative formula

#f'(g(0))g'(0) = f'(0)(3) = 2(3) = 6#

Hopefully this helps!

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