Question

y’(x)=7sin(x+12)/cos(-5x)


Найти производную

Answer 1

y=7sin(x+12)/cos(-5x)  y'=(u/v)'=1/v²[u'v-v'u]
u=7sin(x+12)   u'=7cos(x+12)
v=cos(-5x)=cos5x    v'=-5sin5x
y'=1/cos²5x[7cos(x+12)*cos5x+5sin5x*7sin(x+12)]=
=7[cos(x+12)*cos5x+5sin5x*sin(x+12)]/cos²5x