K For the following composite function, find an inner function \( u=g(x) \) and an outer function \( y=f(u) \) such that \( y=f(g(x)) \). Then calculate \( y=\tan 3 x^{5} \) Identify the inner and outer functions. Choose the correct answer. A. \( u=g(x)=x^{5} \) and \( y=f(u)=3 \tan u \) B. \( u=g(x)=\tan x \) and \( y=f(u)=3 u^{5} \) O. \( u=g(x)=\tan x^{5} \) and \( y=f(u)=3 u \) \( \frac{d y}{d x}=\square \)

\( H(x)=\frac{3}{x^{2}+1} \) dos funciones \( f(x) \) y \( g(x) \) tales que \( (f \circ g)(x)=H(x) \) son:

DERIVADAS DE PRODUCTOS Y COCIENTES 1. \( h(z)=(2-\sqrt{z})\left(3+8 \sqrt[3]{z^{2}}\right) \) 2. \( f(x)=\left(x-\frac{2}{x}\right)\left(7-2 x^{3}\right) \) 3. \( y=\left(x^{2}-5 x+1\right)\left(12+2 x-x^{3}\right) \) 4. \( g(x)=\frac{\sqrt[3]{x}}{1+x^{2}} \) 5. \( Z(y)=\frac{4 y-y^{2}}{6-y} \) 6. \( V(t)=\frac{1-10 t+t^{2}}{5 t+2 t^{3}} \) 7. \( f(w)=\frac{(1-4 w)(2+w)}{3+9 w} \)

5- Qual das seguintes funções é solução da equação diferencial \( y^{\prime \prime}+2 y^{\prime}-3 y=0 \) :

\( \lim _ { x \mapsto 0 ^ { + } } e ^ { ( \frac { 1 } { x } - 1 ) \ln ( x ) } \)

Hallar la derivada de la función \( f(x)=\operatorname{sen}\left(x^{2}-x\right) \)