Our goal for this problem is to compute $\frac{d}{dx}[{\displaystyle \underset{2}{\overset{x^4}{}}}sin(t^4)dt].$

a$)$ Define $F(x)={\displaystyle \underset{2}{\overset{x}{}}}sin(t^4)dt.$ What is $F^{\text{'}}(x)?($Use the Second Fundamental Theorem of Calculus.$)$

$F^{\text{'}}(x)=$

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b$)$ What is $F(x^4)?$

$F(x^4)={\displaystyle \underset{2}{\overset{n}{}}}sin(t^4)dt$ where $n=$

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c$)$ Use part $($b$)$ and the chain rule to find $\frac{d}{dx}[{\displaystyle \underset{2}{\overset{x^4}{}}}sin(t^4)dt].$

$\frac{d}{dx}[{\displaystyle \underset{2}{\overset{x^4}{}}}sin(t^4)dt]=$

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