## Christos 2 years ago Logarithmic differantiation, http://screencast.com/t/fwBW2D9z9E Can you help me out on this please

1. reemii

when there is an $$x$$ in the exponent and want to compute a limit or a derivative, always resort to this technique: $a^{h(x)} = e^{\ln a^{h(x)}} = e^{h(x) \ln a}$ from here you should be able to do something.

2. Christos

were you able to do it??

3. reemii

do you know the "more simple" formula: $$(a^x)' = a^x \ln a$$ ? ($$a>0$$) knowing this you don't need the above trick. (you have to know the derivation of a compound function formula)

4. .Sam.

Let y=f(x) $\Large y=\pi^{sinx}$ ln both sides $\ln(y)=\sin(x)\ln(\pi)$ Differentiate each term $\frac{1}{y}y'=\ln(\pi)\cos(x) \\ \\ y'=yln(\pi)\cos(x) \\ \\ y'=\pi^{sinx}\ln(\pi)\cos(x)$ Got it?

5. Christos

If that's it yea easy enough

6. reemii

("always" means that it works, but there can be simpler ways depending on the problem) $(\pi^{\sin x})' = (\pi^{\sin x} \ln \pi) (\sin x)' = (\pi^{\sin x} \ln \pi) (\cos x)$ (derivation by parts.)