f(x)=6^xlogsubscript2(x)?

Question

what is f'(x)??

(I don't know how to denote a subscript)

Answer 1

Product rule:
f'(x)=log2(x) 6^x ln(6) + 6^x (1/(xln(2))

Answer 2

If you don't like the previous solutions, use logarithmic differentiation:

ln(F(x)) = x*(log_2(x))*(ln 6) = x*((ln x)/(ln 2))*(ln 6). The derivative of the left side is F'(x)/F(x). You can differentiate the right side, then solve for F'(x).

Answer 3

F= log(e) (ln(x) + ln(2))*6x all over x