`f(t) = arcsin(t^2)` Find the derivative of the function

The derivative of a function with respect to t is denoted as f'(t)

The given function:` f(x) = arcsin(t^2) ` is in a form of a inverse trigonometric function.

Using table of derivatives, we have the basic formula:

`d/(dx)(arcsin(u))= ((du)/(dx))/sqrt(1-u^2)`

By comparison, we may let `u = t^2` then `(du)/(dx)= 2t` .

Applying the formula, we get:

`f'(t) =(2t)/sqrt(1-(t^2)^2)`

`f'(t) =(2t)/sqrt(1-t^4) `    as the first derivative of `f(x)=arcsin(t^2)`

Note: `(t^2)^2 = t^(2*2) = t^4` based on the  Law of Exponents: `(x^m)^n = x^(m*n)`