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Find the value of 'a' for which the function f defined as $ f(x) = \left\{ \begin{array} {l l} a\sin \large\frac{\pi}{{2}(n+1)}, & \quad {x \: \leq \: 0} \\ \large\frac{tanx - sinx}{x^3}, & \quad {x \: > 0} \end{array} \right .$ is continuous at x=0. Differentiate \(( x \: cos \: x )^x + ( x\sin\: x )^{\frac{1}{x}}\) w.r.t. \( x \).

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