Question

Find the differential of this function. y=tan(sqrt(t))

Answer 1

your function doesn't make sense
i think it shod be
y=tan (sqrt(t))

Answer 2

sorry that's what I meant

Answer 3

note that this function can be described as ' a function of a function'
- sqrt(t) is a function of t
and tan (sqrt(t)) is a function of sqrt (t)

and its differentiated by the chain rule

Answer 4

(f(g(t))' = f'(g(t)) * g'(t)

g'(t) = (1/2)t^(-1/2)
f'(g(t)) = sec^2 (t^(1/2)))

(note sqrt t = t^(1/2))

Answer 5

now you need to simplify g'(t) * f' (g(t))

Answer 6

need any more help ?