Question

D/dx
`\int\limits^0_x {cos(2 \pi u)} \, du` is

Answer 1

`\displaystyle(\mathrm d)/(\mathrm dx)\int_x^0\cos2\pi u\,\mathrm du=-(\mathrm d)/(\mathrm dx)\int_0^x\cos2\pi u\,\mathrm du=-\cos2\pi x`

by the fundamental theorem of calculus.