Solución

Aplicando la regla de la cadena a h(x)=sec(g(x))h (x) = sec (g (x)) para obtener h′(x)=sec(g(x)  tg(g(x))  g′(x)h'(x) = sec (g (x) \,\,tg (g (x)) \,\,g'(x) En este problema, g(x)=4x5+2xg (x) = 4x^5 + 2x, entonces tenemos g′(x)=20x4+2g ′ (x) = 20x^4 + 2. Por lo tanto, se obtiene h′(x)=sec(4x5+2x)  tg(4x5+2x)  (20x4+2)=h'(x) = sec (4x^5 + 2x) \,\,tg (4x^5 + 2x) \,\,(20x^4 + 2) = =(20x4+2)  sec(4x5+2x)  tg(4x5+2x)=(20x^4 + 2) \,\,sec (4x^5 + 2x) \,\,tg (4x^5 + 2x)