Can someone help me solve this table? A table of values for f,g,f′, and g′ is given below. (a) If F(x)=f(f(x)), find F′(2). (b) If G(x)=g(g(x)), find G′(3).

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Answer 1 · 2018-02-10T06:01:35

# (a) : 20#.

Part (a) :

By the Chain Rule, we have, for #F(x)=f(f(x))#,

#F'(x)=f'(f(x))*f'(x)#.

#:. F'(2)=f'(f(2))*f'(2)#,

#=f'(1)*5...........................................[because," the given table]"#.

#rArr F'(2)=4*5=20#.

Part (b) :

This can be dealt with similarly.