Question #7e670

1 Answer
Apr 8, 2017

212x212x(ln(x)+1)

Explanation:

y=x21x
y=x212x
ln(y)=ln(x212x)=212xln(x)
Take the derivative with respect to x for both sides:
ddxln(y)=ddx(212xln(x))
Using the chain rule for the left-hand side and the product rule for the right-hand side:
dydxy=212(ln(x)+1)
dydx=212(ln(x)+1)y
Since y=x212x:
dydx=212x212x(ln(x)+1)