Verifying derivative rules for logarithmic and exponential functions

[danago]

Hey. I made some quick notes for an upcoming test, and just wanted some verification for a few parts. Could somebody please tell me if these are true:

$$y = \log _a f(x) \Rightarrow y' = \frac{{f'(x)}}{{f(x)\ln a}}$$

$$y = a^{f(x)} \Rightarrow y' = [f'(x)\ln a]e^{f(x)\ln a}$$


Thanks,
Dan.

 

[d_leet]

I'm pretty sure those are both correct.

 

[danago]

ok thanks :)