# A calculus problem by Daniel Thompson

Calculus Level pending

Let $$F$$ be defined by $F(x)=\int_{0}^{x^3}\left (\int_{0}^{y^2} \left (\int_{0}^{z} x^3y^2zt \; \mathrm{d}t \right )\mathrm{d}z \right )\mathrm{d}y$

$$F' \left (\sqrt[7]{2}\right)=\frac{a}{b}$$ for relatively prime positive integers $$a$$ and $$b$$. What is the value of $$a+b$$?

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