Question

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

Answer 1

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!