# Find the derivative of the function. F(t) = e^(2t*sin 2t).

## Question:

Find the derivative of the function.

{eq}\displaystyle F(t) = e^{2t \sin 2t}. {/eq}

## Differentiation in calculus:

The derivative of a function {eq}f{/eq} at a point {eq}x{/eq} is the slope to the tangent line to the graph on that point. When {eq}f{/eq} is the composition of two functions it can be used the chain rule.

The chain rule is used for computing the derivative of the composition of two functions. The chain rule states that: {eq}\dfrac{\ df(u)}{ \ dx} = \dfrac{\ df}{ \ du} \dfrac{\ du}{ \ dx}. {/eq}

## Answer and Explanation:

We are given:

{eq}F(t) = e^{2t \sin(2t)} {/eq}

Differentiating both sides, we'll get:

{eq}\Rightarrow \displaystyle \dfrac{\ dF }{ \ dt }=...

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