# How do you find the derivative of #g(x) = int 9*sqrt(1+t^8)dt# from 7 to #x^2#?

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To find the derivative of ( g(x) = \int_{7}^{x^2} 9\sqrt{1+t^8} , dt ), you can use the Fundamental Theorem of Calculus. According to this theorem, if ( g(x) ) is defined as the integral of a function ( f(t) ) from a constant ( a ) to ( x ), then ( g'(x) = f(x) ).

So, to find ( g'(x) ), you need to evaluate ( f(x) ), where ( f(t) = 9\sqrt{1+t^8} ), and then substitute ( x^2 ) into this function.

After finding ( f(x) ), you can differentiate it with respect to ( x ). The resulting expression will be ( g'(x) ), the derivative of ( g(x) ).

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