Kann man hier was zusammenfassen 2

Question

f´(x)= 1/ln(4)x   * log2(x) + log4(x)  * 1/ln(2)x

Was kann hier ausklammern ?

Answer 1

Soll das vielleicht so heißen: f´(x)= 1/ln(4)x  * log₂(x) + log₄(x)  * 1/ln(2)x? Dann gilt:

f´(x)= 1/ln(4)x  * ln(x)/ln(2) + ln(x)/ln(4)  * 1/ln(2)x.

Answer 2

Aloha :)

$$\frac{1}{\ln(4)x}\cdot\log_2(x)+\log_4(x)\cdot\frac{1}{\ln(2)x}$$$$=\frac{1}{\ln(4)x}\cdot\frac{\ln(x)}{\ln(2)}+\frac{\ln(x)}{\ln(4)}\cdot\frac{1}{\ln(2)x}$$$$=\frac{1}{\ln(4)\ln(2)}\cdot\frac{\ln(x)}{x}+\frac{1}{\ln(4)\ln(2)}\cdot\frac{\ln(x)}{x}$$$$=\frac{2}{\ln(2^2)\ln(2)}\cdot\frac{\ln(x)}{x}$$$$=\frac{2}{2\ln(2)\ln(2)}\cdot\frac{\ln(x)}{x}$$$$=\frac{1}{\ln^2(2)}\frac{\ln(x)}{x}$$