$\begin{array}{l}a)\,\,y = 5^{x^2 -1}.\sin2x\\ \to y' = (5^{x^2-1})'.\sin2x +5^{x^2 - 1}.(\sin2x)' \\ \to y' = 2x.5^{x^2-1}.\ln5\sin2x + 5^{x^2-1}.2\cos2x\\ \to y' = 2.5^{x^2-1}(x\ln5\sin2x + \cos2x)\\ b)\,\,y = \dfrac{\log5^3}{x^2}\\ \to y' = 3\log5.\left(\dfrac{1}{x^2}\right)'\\ \to y' = -3\log5\cdot\dfrac{2x}{x^4}\\ \to y' = -\dfrac{6\log5}{x^3}\end{array}$
