Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

ok got it thanks you so much

Answer 7

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

Answer 8

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