Question

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.

Answer 1