Question

Find the derivative using logarithmic differentiation or implicit
differentiation :
U=√(t+1)/∛(t-1)

Answer 1

where do you need help?

Answer 2

Take logs of both sides

Recall \[\log(x^n)=n logx\]

Then also use the result
\[\ln(y) = f(x) \rightarrow \frac{ d }{ dx } \ln(y) = \frac{ d }{ dy }\ln(y)\frac{ dy }{ dx } = \frac{ d }{ dx }f(x) \]
\[\frac{ d }{ dy }\ln(y) \frac{ dy }{ dx } = \frac{ 1 }{ y } \frac{ dy }{ dx } = f'(x) \rightarrow \frac{ dy }{ dx } = yf'(x)\]