Calc2.15

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f(x)=\int _{{x^{2}}}^{{3x^{4}}}\cos(t)\,dt\,

Again, we use the Second Fundamental Theorem along with the Chain Rule. Most calculus books have very few examples of this type of problem. A general formula for this would be

{\frac  {d}{dx}}\left[\int _{{a(x)}}^{{b(x)}}g(t)\,dt\right]=g(b(x))b'(x)-g(a(x))a'(x)\,

So, here, we have

f'(x)=\cos(3x^{4})(12x^{3})-\cos(x^{2})(2x)\,


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