Find the slope at any value of x,if y=(x)^lnx?

1 Answer
May 27, 2018

The slope at any value of #x# is given by #x^lnx(2/xlnx)#

Explanation:

This question is pretty much asking for the derivative of #y#. We will use logarithmic differentiation for this, aka take the logarithm of both sides of the function.

#lny = ln(x^lnx)#

Now apply the logarithm property that states #ln(a^n) = nlna#.

#lny = lnxlnx#

#1/y(dy/dx) = 1/xlnx + 1/xlnx#

#1/y(dy/dx) = 2/xlnx#

#dy/dx = y(2/xlnx)#

#dy/dx= x^lnx(2/xlnx)#

Hopefully this helps!