Question

Use logarithmic differentiation to determine the derivative of f(x)=(x^7(x-9)^6/(x^2+4)^8

Answer 1

i have worked out the first part this is what i have so far lny=7lnx+6ln(x-9)-8ln(x^2+4)

Answer 2

I can't read functions not in latex form :P

\[\Large y = \frac{x^7(x-9)^6 }{ (x^2+4)^8 }\]

\[\Large \ln y = 7 \ln x + 6 \ln (x-9) - 8 \ln (x^2+4)\]
excellent, yours looks correct so far. Now differentiate.

Answer 3

umm this is where i stop since ln y is y'/y then i multiplied the other side by y so i got y'=[7/x+6/(x-9)-16x/(x^2+3)][x^7(x-9)^6/(x^2+4)^8

Answer 4

Yeah i can't read that :P but it looks like this

\[\Large \left( \frac{ 1 }{ y } \right) \frac{ dy }{ dx }= \frac{ 7 }{ x } + \frac{ 6 }{ x-9} - \frac{ 16x }{ x^2+4} \]

\[\Large \frac{ dy }{ dx }= \frac{x^7(x-9)^6 }{ (x^2+4)^8 } \left( \frac{ 7 }{ x } + \frac{ 6 }{ x-9} - \frac{ 16x }{ x^2+4} \right)\]

except you have an x^2+3 that should be x^2+4

Answer 5

no wonder it kept marking it wrong thanks for pointing it out :)