calculate and simplify the differentials with respect to x of the foll

Question

Calculate and simplify the differentials with respect to x of the following. Be sure to show all your calculations, not only the final answers. \text { a) } y=(x-4)(x+5)(x-1) \text { b) } \quad y=\frac{x}{1-x^{2}} \text { c) } y=\sqrt{x}-\frac{1}{\sqrt{x}} \text { d) } \quad y=(x-1)^{3} \text { e) } 3 x^{2} \cos (x) \text { f) } y=\frac{(3 x+2)^{3}}{(2 x-1)^{2}} \text { g) } y=\sin ^{3}(2 x) \text { h) } \quad y=\ln (\sin (x)) \text { j) } y=3 \tan (x) \text { i) } y=e^{x^{2}}(x-1)^{3}