# 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))#