Question

[lnx]^7 FIND the derivative

Answer 1

Use the chain rule:

\[\Large y = (\ln x) ^7\]
Multiply by the power (7), reduce the power by one, then multiply by the derivative of the inside function (derivative of lnx is 1/x)
\[\Large y \prime = 7 (\ln x) ^6 \left( \frac{ 1 }{ x } \right)\]

Answer 2

do i have to simplify the ln(x) further

Answer 3

You can't. You can just move the 1/x \[\Large y \prime = \frac{ 7 }{ x } (\ln x) ^6 \]