[MATH][/MATH]Hello,
I am working through some logarithmic differentiation problems. The following example was presented:
Differentiate y = xx(1/2)
Using the logarithmic differentiation and the product rule, the example provides the answer:
y' = xx(1/2)[(2 + ln x) / 2x(1/2)]
Why can't I do the following instead?
y = xx(1/2)
logxy = logxxx(1/2) = x(1/2)
(1/(y ln x))y' = (1/2)x-(1/2)
y' = (y ln x)/(2x(1/2))
(substituting the first equation for y):
y' = xx(1/2)(ln x/2x(1/2))
which as far as I can tell does not agree with the above method. Any help is appreciated!
(ref: Stewart, J. Calculus, Early Transcendentals (5th ed). Belmont, CA, Brooks/Cole, 2003. Page 247.)
I am working through some logarithmic differentiation problems. The following example was presented:
Differentiate y = xx(1/2)
Using the logarithmic differentiation and the product rule, the example provides the answer:
y' = xx(1/2)[(2 + ln x) / 2x(1/2)]
Why can't I do the following instead?
y = xx(1/2)
logxy = logxxx(1/2) = x(1/2)
(1/(y ln x))y' = (1/2)x-(1/2)
y' = (y ln x)/(2x(1/2))
(substituting the first equation for y):
y' = xx(1/2)(ln x/2x(1/2))
which as far as I can tell does not agree with the above method. Any help is appreciated!
(ref: Stewart, J. Calculus, Early Transcendentals (5th ed). Belmont, CA, Brooks/Cole, 2003. Page 247.)