Find F'(t) given F(t) = sin^-1(x) * (sqrt(sin(t)))

Question

i dont understand this at all!! help me with this asap!!

Answer 1

F(t) = sin^-1(x)*√sin(t)

 

I am assuming that x is also a function of t: x = x(t).  Use the product rule for differentiation:

 

 

F'(t) = (dx/dt)/√(1-x²)*√sin(t) + sin^-1(x)*cos(t)/(2√sin(t))

 

 

We have used

 

d/dt (sin^-1u) = 1/√(1 - u²) du/dt,

 

d/dt √u = 1/(2√u) du/dt,

 

and d/dt sin(u) = cos(u) du/dt.