Question

Usando as regras de derivação e da cadeia, obtenha f'(x) em cada caso:
I. f(x)= (x^3+4)^4
II. f(x)=√(x^2)-7
III. f(x)=e^sin(x)

Answer 1

I.
$f(x) = (x^3 + 4)^4 f'(x) = 4 * (x^3 + 4)^3 * (x^3 + 4)' f'(x) = 4 * (x^3 + 4)^3 * (3x^2 + 0) f'(x) = 4 * (x^3 + 4)^3 * (3x^2) f'(x) = 12x^2 (x^3 + 4)^3$


II.
$f(x)=\sqrt{x^2-7} f(x) = (x^2 - 7)^{1/2} f'(x) = {1/2} * (x^2 - 7) ^{1/2 - 1} * (x^2 - 7)' f'(x) = {1/2} * (x^2 - 7) ^{-1/2} * (2x) f'(x) = ({1/2} * (2x)) * (x^2 - 7) ^{-1/2} f'(x) = (x) * (x^2 - 7) ^{-1/2} f'(x) = x/\sqrt{x^2 - 7}$

III.
$f(x)=e^{sin(x)} f'(x) = (sin(x))' * e^{sin(x)} f'(x) = cos(x) * e^{sin(x)}$