यदि `f(x)=|cosx-sinx|`, `f'((pi)/(2))` ज्ञात करें ।

Explanation

जब `oltxlt(pi)/(4),cosxgtsinx`
`thereforecosx-sinxgt0`
तथा जब `(pi)/(4)ltxlt(pi)/(2),cosxltsinx`
`thereforecosx-sinlt0`
जब `(pi)/(2)ltxltpi,cosx-sinxlt0`
`therefore` जब `(pi)/(4)ltxltpi,cosx-sinxlt0`
`therefore|cosx-sinx|=-(cosx-sinx)`
अतः `f(x)=-cosx+sinx`,जब `(pi)/(4)ltxltpi`
`thereforef'(x)=sinx+cosx`
`thereforef'((pi)/(2))="sin"(pi)/(2)+"cos"(pi)/(2)=1+0=1`