Question

How do you use the chain rule to differentiate `root11(lnx)`?

Answer 1

`1/(11x(lnx)^(10/11))`

Explanation:

This can be written as:

`y=(lnx)^(1/11)`

Which can be differentiated using the chain rule. The outside function is `x^(1/11)`, whose derivative is `1/11x^(-10/11)`. The derivative of the inside function, the inside function being `lnx`, is `1/x`.

So, the chain rule tells us that:

`dy/dx=1/11(lnx)^(-10/11)*1/x`

`dy/dx=1/(11x(lnx)^(10/11))`