Question

Find f '(0.3) for f of x equals the integral from 0 to x of the arccosine of t, dt

Answer 1

By the fundamental theorem of calculus,

`\displaystyle(\mathrm d)/(\mathrm dx)\int_0^x\cos^(-1)t\,\mathrm dt=\cos^(-1)x`

so that

`f'(0.3)=\cos^(-1)0.3\approx1.266`