# Diffrentiate or integrate? I'm so confused

Calculus Level 4

Let $$f$$ be a real valued function defined on the interval $$(-1,1)$$ such that $$\displaystyle { e }^{ -x }f\left( x \right) =2+\int _{ 0 }^{ x }{ \sqrt { { t }^{ 4 }+1 } \, dt }$$ for all $$x\in(-1,1)$$and let $$f^{ -1 }$$ be the inverse function of $$f$$. Then find the value of $$3{ ({ f }^{ -1 }) }^{ { ' } }\left( 2 \right)$$ where $$(')$$ represents $$\frac { dy }{ dx }$$.

×