Question

what is differentiation of e^xcosx ( cosx - xsinx )
please explain step by step​

Answer 1

$y = {e}^{x} cosx(cosx - sinx) \\ \\ \frac{dy}{dx} = {e}^{x} cosx \frac{d}{dx} (cosx - sinx) + \\ {e}^{x} (cosx - sinx) \frac{d}{dx} cosx + \\ cosx(cosx - sinx) \frac{d}{dx} {e}^{x} \\ \\ \frac{dy}{dx} = {e}^{x} cosx( - sinx - cosx) + \\ {e}^{x} (cosx - sinx)( - sinx) + \\ cosx(cosx - sinx) {e}^{x} \\ \\ \frac{dy}{dx} = - {e}^{x} cosx(cosx + sinx) \\ + {e}^{x} (cosx - sinx)( - sinx + cosx) \\ \\ \frac{dy}{dx} = - {e}^{x} cosx(cosx + sinx) + \\ {e}^{x} ( {cosx - sinx})^{2}$