How do you differentiate y=x^x?
To solve this problem, you need to put it into simplest form which is putting it into natural logarithm both the RHS and LHS. Then differentiate both side with respect to x as shown below.
In(y) = ln(x^x) - natural logarithm both side
ln(y) = xln(x) - using the power rule
(1/y)dy/dx = x*1/x + ln(x) - Diffrentiate both side (chain rule in the RHS)
dy/dx = y(1+ln(x)) - multiplying 'y' in both sides
= x^x(1+ln(x)) - replacing the value of 'y'
MT
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