How do you differentiate #f(t)=sin^2(e^(sin^2t))# using the chain rule?
So, we got three functions here:
and
This will be the differentiated function.
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Please see the explanation below.
So we need the derivative of a square and we'll need the chain rule.
Combining all of this into one calculation:
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To differentiate ( f(t) = \sin^2(e^{\sin^2t}) ) using the chain rule:

Find the derivative of the outer function with respect to its inner function. [ \frac{d}{dt}[\sin^2(u)] = 2\sin(u)\cos(u) ]

Find the derivative of the inner function with respect to the variable ( t ). [ \frac{d}{dt}[e^{\sin^2t}] = e^{\sin^2t} \cdot 2\sin(t)\cos(t) ]

Multiply the results from steps 1 and 2. [ 2\sin(e^{\sin^2t})\cos(e^{\sin^2t}) \cdot e^{\sin^2t} \cdot 2\sin(t)\cos(t) ]

Simplify the expression if necessary.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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