Derivatives products chain and rule

Question

Find the derivative of 

Answer 1

Let u = 5t⁴. Because the derivative of ln(x) is 1/x, then the derivative of ln(u) is 1/u, or 1/(5t⁴)_, HOWEVER, since u is a function in "t", the chain rule requires we multiply by the derivative of u with respect to t (which is 20t³).

So g'(t) = 1/(5t⁴)•20t³ = 20t³/5t⁴ = 4/t