Question

Determine DxY.
y=logx/x

Answer 1

DxY = dy/dx

y = (1/x) * log x

y = (1/x) * log e * log x /log e

y = (1/x) * log e * ln(x)

y = log e   * (1/x) * ln(x)

y'= log e * [ (1/x)' * ln(x) +  (1/x) * (ln(x))']

y'= log e  * [ -1/x² * ln(x) + (1/x) * (1/x)]

y'= log e  * [ -1/x² * ln(x) + (1/x²)]