Question

Aplica la regla de cadena para derivar las sigientes funciones
A - f: - f(x) = sen (x2 + 5)
B- f:- f(x) = ln (sen x)
C-f:- f(x) = cos2 (x3+2x3)

Answer 1

A) $f(x)=sen(x^{2} +5)\\f'(x)=cos(x^{2} +5)(2x)\\f'(x)=2xcos(x^{2} +5)$

B) $f(x)=ln(senx)\\f'(x)=\frac{1}{senx} cosx\\f'(x)=\frac{cosx}{senx}$

C) $f(x)=cos^{2} (x^{3}+2x^{3}  )\\f(x)=cos^{2} (3x^{3}  )\\f'(x)=2(cos (3x^{3})  )(-sen(3x^{3} ))(9x^{2} )\\f'(x)=-18x^{2} (cos (3x^{3} ) )(sen(3x^{3} ))\\f'(x)=-18x^{2} (cos (3x^{3})  )(sen(3x^{3} ))\\f'(x)=-9x^{2} sen(6x^{3} )$