Find the derivative of d/dx [ln(lnx)+lnx]?

Answer 1

By using the property of linearity of the derivative, the derivative of the given function can be written as

d/dx(ln(ln(x))) + d/dx(ln(x))

By applying the chain rule, the derivative of the first term is 1/ln(x)*d/dx(ln(x))=1/ln(x) * 1/x while the derivative of the second term is 1/x.

Therefore, the derivative of the given function is 1/x*(1/ln(x) +1) or 1/(x*ln(x)) +1/x

Best,

Davide