engineering mathematics MCQ #783

Find the derivative of y = x^(1/x)

engineering mathematics MCQ #783

  1. Question 1

    Q1. Find the derivative of y = x^(1/x)

    • A) x^(1/x) (1 - ln(x)) / x²
    • B) x^(1/x) (1 + ln(x)) / x²
    • C) x^(1/x - 2) (1 - ln(x))
    • D) x^(1/x) (1 - ln(x))

    Answer: x^(1/x - 2) (1 - ln(x))

    Explanation: Take ln(y) = ln(x)/x, then differentiate implicitly to get (1/y)dy/dx = (1 - ln(x))/x², so dy/dx = y(1 - ln(x))/x² = x^(1/x) (1 - ln(x))/x² = x^(1/x - 2) (1 - ln(x))