anonymous 5 years ago Use logarithmic differentiation to find the derivative of the function: y=(5x-4)^4 (x^5-6)^7 (7x^8+9)^9

1. anonymous

ln y=4ln(5x-4) etc

2. anonymous

like chguanas said. take the log. simplify using properties of the log. then take the derivative of that, then multiply by the original mess. $4ln(5x-4)+7ln(x^5-6) +9ln(7x^8+9)$

3. anonymous

derivative is $\frac{20}{5x-4}+\frac{35x^4}{x^5-6}+\frac{504x^7}{7x^8+9}$

4. anonymous

so something like this: 4 * (1/(5x-4)) * 5/1

5. anonymous

then just write that times the origial thing and you are done.

6. anonymous

ok got it thanks you so much

7. anonymous

yeah chain rule. derivative of $ln(f(x))=\frac{f'(x)}{f(x)}$

8. anonymous

I have a final tomorrow and was really scare for that one