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Find the derivative of \(\displaystyle F(x) = \int\limits_{-6}^{x} \cos{\left(t \right)}\, dt\).

Using the Fundamental Theorem of Calculus part I gives \(\displaystyle F'(x)=\cos{\left(x \right)}\).

\begin{question}Find the derivative of $F(x) = \int\limits_{-6}^{x} \cos{\left(t \right)}\, dt$. 
    \soln{9cm}{Using the Fundamental Theorem of Calculus part I gives $F'(x)=\cos{\left(x \right)}$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)

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\begin{document}\begin{question}(10pts) The question goes here!
    \soln{9cm}{The solution goes here.}

\end{question}\end{document}

Find the derivative of <img class="equation_image" title=" \displaystyle F(x) = \int\limits_{-6}^{x} \cos{\left(t \right)}\, dt " src="/equation_images/%20%5Cdisplaystyle%20F%28x%29%20%3D%20%5Cint%5Climits_%7B-6%7D%5E%7Bx%7D%20%5Ccos%7B%5Cleft%28t%20%5Cright%29%7D%5C%2C%20dt%20" alt="LaTeX: \displaystyle F(x) = \int\limits_{-6}^{x} \cos{\left(t \right)}\, dt " data-equation-content=" \displaystyle F(x) = \int\limits_{-6}^{x} \cos{\left(t \right)}\, dt " /> .

Using the Fundamental Theorem of Calculus part I gives <img class="equation_image" title=" \displaystyle F'(x)=\cos{\left(x \right)} " src="/equation_images/%20%5Cdisplaystyle%20F%27%28x%29%3D%5Ccos%7B%5Cleft%28x%20%5Cright%29%7D%20" alt="LaTeX: \displaystyle F'(x)=\cos{\left(x \right)} " data-equation-content=" \displaystyle F'(x)=\cos{\left(x \right)} " /> .