Find $F^{\prime}(x)$ if the following is true: \[ F(x)=\int_{0}^{x} \frac{1}{1+t^{5}} d t \] a. $\ln \left(1+x^{5}\right)$ b. $\frac{x^{4}}{1+x^{5}}$ c. $\ln x^{4}$ d. $\frac{1}{1+x^{5}}$

Step 1 ：The problem is asking for the derivative of the function \(F(x)\), which is defined as an integral from 0 to \(x\) of the function \(\frac{1}{1+t^{5}}\).

Step 2 ：According to the Fundamental Theorem of Calculus, if a function \(F(x)\) is defined as an integral of a function \(f(t)\) from a constant to \(x\), then the derivative of \(F(x)\) is simply \(f(x)\).

Step 3 ：Therefore, the derivative of \(F(x)\) should be \(\frac{1}{1+x^{5}}\).

Step 4 ：Final Answer: The derivative of the function \(F(x)\) is \(\boxed{\frac{1}{1+x^{5}}}\).