Question

Use logarithmic differentiation to find the derivative of the function y = x^x

Answer 1

(1+logx)x^x

Answer 2

y = x^x

ln both sides...

lny = lnx^x

via reverse power rule...

lny = xlnx

you can use implicit differentiation now...you do know that right/

Answer 3

so d/dx(lny) = 1/y * y' and d/dx(xlnx) = x*1/x .....????

Answer 4

it goes lyk tis logy= xlogx
diff wrt to x on bth sides so on lhs its 1/y dy/dx=1+logx by product rule on rhs u get 1+logx
thn dy/dx =(1+logx)y wer y is nthin bt =x^x

Answer 5

one of my favourite derivatives. an alternative to the ones suggested above:
y = e^log(x^x) = e^xlog(x) which you can differentiate using the chain rule

Answer 6

thx guys you just walked me through my first ever log diff problem