Solve: x(sinx – cosx). – InterviewSolution

1.	Solve: x(sinx – cosx).
Answer» Let y = x^{(sinx – cosx)}; log y = (sin x – cos x) log x diff w.r.t x. \(\frac{1}{y}\frac{dy}{dx}\) = (sinx – cosx) .\(\frac{1}{x}\) + logx (cosx + sinx); \(\frac{dy}{dx}\) = y [\(\frac{sinx - cosx}{x}\) + log x.(cosx + sinx)]

Solve: x(sinx – cosx).

Answer»

Let y = x^{(sinx – cosx)}; log y = (sin x – cos x)

log x diff w.r.t x.

\(\frac{1}{y}\frac{dy}{dx}\) = (sinx – cosx) .\(\frac{1}{x}\) + logx (cosx + sinx);

\(\frac{dy}{dx}\) = y [\(\frac{sinx - cosx}{x}\) + log x.(cosx + sinx)]