Let y = xsin x + cos x⇒ log y = log xsin x + cos x⇒log y = sin x + cos x log x⇒1ydydx = sin x + cos x × 1x + log xcos x - sin x⇒dydx = ysin x + cos xx + log xcos x - sin x⇒dydx = xsin x + cos xsin x + cos xx + log xcos x - sin x

x^{sinx + cosx}

Let y = x^{\sin x + \cos x} \Rightarrow \log y = \log [x^{\sin x + \cos x}] \Rightarrow \log y = (\sin x + \cos x) \log x \Rightarrow \frac{1}{y} \frac{d y}{d x} = (\sin x + \cos x) \times \frac{1}{x} + \log x (\cos x - \sin x) \Rightarrow \frac{d y}{d x} = y [\frac{\sin x + \cos x}{x} + \log x (\cos x - \sin x)] \Rightarrow \frac{d y}{d x} = x^{\sin x + \cos x} [\frac{\sin x + \cos x}{x} + \log x (\cos x - \sin x)]

View Full Answer

xsinx + cosx

x^{sinx + cosx}