Question

find dy/dx using log differentiation for y = x(x-1)^(3/2) / sqrt(x^2 +1)

Answer 1

log y= logx+3/2log(x-1) -1/2log(x^2+1)

Answer 2

1/y dy/dx=1/x +3/2 (1/x-1)-1/2(1/(x^2+1) (2x)

Answer 3

\[\frac{dy}{dx}=[\frac{1}{x}+\frac{3}{2(x-1}-\frac{x}{x^{2}+1} ] \frac{x(x-1)^{3/2}}{\sqrt{x^{2}+1}}\]

Answer 4

using log properties log(xy)=logx+logy....... log (x/y) = logx=logy........log(x^y)=ylogx

Answer 5

whoops log (x/y)= logx-logy