The derivative of the function f(x) as given in the task content by virtue of the Fundamental theorem of calculus is; f'(x) = -√(7 + sec(4t).
What is the derivative of the function f(x) by virtue of the Fundamental theorem of calculus as given in the task content?
It follows from the image attached to the task content that;
f(x) = Integral; √(7 + sec(4t) dt (with the upper and lower limits 0 and x respectively).
It also follows from the hint given that the integral can be written in another form with the the negative sign and the limits reversed.
However, since it follows from the Fundamental theorem of calculus that given an integral; where;
g(x) = Integral f(t) ft with limits a and x, it follows that the differential of g(x); g'(x) = f(x).
Consequently, the function f'(x) which is to be evaluated in this scenario can be determined as;
f'x = - √(7 + sec(4t) .
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