How do you differentiate f(t)=sin^2(e^(sin^2t)) using the chain rule?
2 Answers
Explanation:
So, we got three functions here:
and
Let
differentiating w.r.t.
This will be the differentiated function.
Please see the explanation below.
Explanation:
sin^2(u) which is also(sin(u))^2
So we need the derivative of a square and we'll need the chain rule.
= 2sin(u)cos(u) d/dt(u)
In this problem,
So,
= e^(sin^2t)*[2sintcost]
Combining all of this into one calculation:
= 4sintcost * e^(sin^2t)sin(e^(sin^2t))cos(e^(sin^2t))
Because
= [2sintcost] * [e^(sin^2t)][2sin(e^(sin^2t))cos(e^(sin^2t))]
= sin(2t) e^(sin^2t)sin(2e^(sin^2t))