Question

Question 9: (sin x – cos x)^ (sin x – cos x), π/4 < x < 3π /4

Class 12 - Math - Continuity and Differentiability

Answer 1

y = (sinx-cosx)^sinx-cosx
:• logy = (sinx - cosx) log (sinx-cosx)

Differentiating w.r.t x
1/y dy/dx = (sinx-cosx).1/sinx-cosx .(cosx+sinx) +log(sinx-cosx).(cosx + sinx)
= cosx+sinx+(cosx+sinx)log(sinx-cosx)

:• dy/dx = y[cosx+sinx {1+log(sinx-cosx)}]
= (sinx-cosx)^sinx-cosx [cosx+sinx {1+log(sinx-cosx)}].