Calculate dy/dx: y=sqrt (t ln(t^4))?

Question

Calculate dy/dx: y=sqrt (t ln(t^4))?

Answer 1

There is no way you can find dy / dx just from a formula relating y and t.

y = [  t ln(t^4) ]^(1 / 2)

(d / dt) ln(t^4) = 4t^3 / ln(t^4)

dy / dt = (1 / 2) [ t ln(t^4) ]^(- 1 / 2) * [ t * 4t^3 / ln(t^4) + ln(t^4) ]

= [ 4t^4 / ln(t^4) + ln(t^4) ] / { 2 sqrt[ t ln(t^4) ] }.

= [ 4t^4 + {  ln(t^4) }^2 ] / [ 2 ln(t^4) sqrt[ t ln(t^4) ].