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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)=_______

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Solution Summary

Chain and Quotient rules are also integrated.

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