Posted by **Sunny** on Wednesday, May 1, 2013 at 10:27pm.

Find f’(x) if f(x) = 3^g(x) where g(x) = LOG_3(x^2 - √x + 4/x + 10*LOG_e(x))

- math -
**Reiny**, Wednesday, May 1, 2013 at 10:46pm
if f(x) = 3^g(x)

then f'(x) = (ln3)(3^(gx)) (g ' (x) )

g(x) = ???? , do you mean 3 to be the base of LOG

or are we doing ln ? or what

Once you have decided, continue as below ...

so g ' (x) = ....

insert that result above.

- math -
**Sunny**, Wednesday, May 1, 2013 at 10:55pm
the 3 is the base so log(base3)(...log(base/e)(x)

- math -
**Steve**, Thursday, May 2, 2013 at 12:03pm
if g(u) = log_3(u)

f(x) = 3^g(u) = 3^log_3(u) = u

so now it's easy:

f(x) = x^2 - √x + 4/x + 10*ln(x)

f'(x) = 2x - 1/(2√x) - 4/x^2 + 10/x

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