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Composition question

If f(0)=1, f'(0)=2, g(0)=3, g'(0)=4 what is (f^2•g)'(0) 


Are you sure the question is written correctly?

Faith, it's not clear what f^2 means. It could mean f(x) times f(x), but sometimes f^2 also means f(f(x)), i.e. f composed with itself. Do you know which it is?

sorry for the lack of information, I just copied down what my teacher had on the worksheet. 

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2 Answers


(uv)' = uv' +vu', and remember Mr. Chain.

(f^2•g)'(0) = 2f(f')g + f^2(g'), all evaluated at 0.

2 f(0)(f'(0))(g(0)) + (f(0))^2(g'(0))  =

2(1)(2)(3) + 1^2(4) =  12 + 4 = 16