Question

How do I take the derivative of ln [(x(x^2+2))/sqrt(x^3-7)]?

Answer 1

hi use the log property ln(a)/(b)=ln(a)-ln(b)

Answer 2

there \[a=x(x^2+2)\]
and
\[b=\sqrt{x^3-7}\]

Answer 3

You could also do it directly, working from the ln back inwards. I'll do the first step:\[\left(\ln \left( \frac{ x(x^2+2) }{ \sqrt{x^3-7} } \right)\right)'=\frac{ 1 }{ \frac{ x(x^2+2) }{ \sqrt{x^3-7} } }\cdot\left( \frac{ x(x^2+2) }{ \sqrt{x^3-7} }\right)'=\]\[\frac{ \sqrt{x^3-7} }{ x(x^2+2)}\cdot \left( \frac{ x^3+2x }{ \sqrt{x^3-7} } \right)'=...\]Now you have to use the Quotient Rule for the part on the right...

Answer 4

You can see that it's a eather ugly thing. If you use @muhammad9t5's trick, there are no fractions anymore, so everything becomes much easier!

Answer 5

now it will become

\[\ln x(x^2+2)-\ln(\sqrt{x^3-7}\]