Discuss the below:
Q: Find the derivatives of the following functions, and simplify into the forms specified.
(a) g(x)=x^(12) (9 ln x + 15)
The derivative of g(x) can be expressed in the form g'(x)=x^(11) h(x), where h(x) is some function of x. Find h(x).
h(x)=_______
(b) y= ln (3e^(9x) + x^6)
dy/dx=______
(c) f(x) = (6 ln x)/5 ln x + 6
The derivative of f(x) can be expressed in the form f '(x)= (k(x))/x(5 ln x + 6)^2 where k(x) is some function of x. Find k(x).
k(x)=______
(d) r(x)=7ln(tanx+secx)+ln(2tanx)+8ln(secx).
r'(x)=_______