Differentiate x^cos(x) and find the derivative of cosec^-1(x)
for part a) let y=xcos(X) , the ln(y)=ln(xcos(X))=cos(x)ln(x), thus d/dx (ln(y(x)) = d/dx (cos(x)ln(x)), 1/y*dy/dx=cox(x)/x - sinxlnx => solve for dy/dx => y'(x)=xcos(X) (cox(x)/x - sinxlnx) b) d/dx cosec-1(x)= -1/x(x2 -1)1/2 this is shown by setting y as the function, rearrange for x then doing implict differentiation to solve for dy/dx in terms of y, then use the defenintions of sine to express in terms of x
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