Given:
[tex]f(x)=\int_0^{x^2}t^2dt[/tex]
Required:
The value of
[tex]f^{\prime}(x)[/tex]
Explanation:
Let us solve the integral.
[tex]\begin{gathered} f(x)=\int_0^{x^3}t^2dt \\ \Rightarrow[\frac{t^3}{3}] \\ =\frac{x^9}{9}+c \end{gathered}[/tex]
Thus,
[tex]f^{\prime}(x)=x^8[/tex]
Final Answer:
The derivative is,
[tex]f^{\prime}(x)=x^8[/tex]
