# Think outside the box (3)

Calculus Level 4

Let $$f^{(0)}(x) = (5x^3+99x^{98}+2)^{100}$$, where $$f^{(n)}(x)$$ denotes the $$n^\text{th}$$ derivative of $$f(x)$$. If the value of $$f^{(98)}(0)$$ is in the form $$(a^2)!\times b^{99}$$, where $$a$$ and $$b$$ are natural numbers . Find the value of $$a+b$$.

 Notation: $$!$$ is the factorial notation. For example, $$8! = 1\times2\times3\times\cdots\times8$$.

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