5.3 The Fundamental Theorem of Calculus/7: Difference between revisions
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<math>g(x)=\int_{1}^{x}\frac{1}{t^3+1}dt</math><br> | <math>g(x)=\int_{1}^{x}\frac{1}{t^3+1}dt</math><br> | ||
<math>\frac{d}{dx}\left[g(x)\right]=\frac{d}{dx}\left[\int_{1}^{x}\frac{1}{t^3+1}dt\right] | <math>\frac{d}{dx}\left[g(x)\right]=\frac{d}{dx}\left[\int_{1}^{x}\frac{1}{t^3+1}dt\right]= | ||
(1)\left(\frac{1}{1+x^3}\right)=\frac{1}{1+x^3}</math> | (1)\left(\frac{1}{1+x^3}\right)=\frac{1}{1+x^3}</math> | ||
Revision as of 19:43, 25 August 2022
![{\displaystyle {\frac {d}{dx}}\left[g(x)\right]={\frac {d}{dx}}\left[\int _{1}^{x}{\frac {1}{t^{3}+1}}dt\right]=(1)\left({\frac {1}{1+x^{3}}}\right)={\frac {1}{1+x^{3}}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/5cf560a961e2c0da347690da04642fcc62a95391)