Question

# Having knowledge of composite functions, we know that the mastery of some functions are the image...

Having knowledge of composite functions, we know that the mastery of some functions are the image of others, that is, a composite function H (x) can be given by H (x) = f (g (x)). Many functions of this type are transcendent, meaning that they have no algebraic formulation. Given that if f (x) = sen (x), f ’(x) = cos (x), and considering your knowledge of the chain rule for derivation of composite functions, analyze the following statements.

I. The derivative of f (x) = (x + 2) ² is 2x + 4.

II. The function H (x) = f (g (x)), where f (x) = sen (x) and g (x) = x² + x, has derivative H '(x) = (2x + 1) * cos ( x² + x).

III. To derive transcendent functions just apply the rules for derivatives of polynomial functions. IV. The derivative of f (f (x)) is equal to cos² (x) sen (x). Only what is stated in:

1. II, e IV.

2. I e III.

3. I, III e IV.

4. I e II.

5. I, II e IV.

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