f(x) is a xomposite of two functions
Let :
color(blue)(g(x)=3x-1) and color(brown)(h(x)=cscx
So,
f(x)=color(brown)hcolor(blue)((g(x))
so thederivative of this function is by applying chain rule:
color(red)(f'(x))=color(red)(h'(g(x)*(g'(x))
color(red)h'(g(x))=????
color(brown)(h(x)=cscx
h'(x)=cosx*csc^2x
color(red)h'(g(x))=cos(g(x))*csc^2(g(x))=cos(3x-1)*csc^2(3x-1)
color(red)(h'(g(x))) = cos(3x-1)*csc^2(3x-1)
color(red)(g'(x))=????
color(blue)(g(x)=3x-1)
color(red)(g'(x))=3
color(red)(f'(x))=color(red)(h'(g(x)*(g'(x))
color(red)(f'(x))=cos(3x-1)*csc^2(3x-1)*3
color(red)(f'(x)=3cos(3x-1)csc^2(3x-1))
