Use logarithmic differentiation to calculate the derivative.
F(x)=x^sqrtx

Question

Use logarithmic differentiation to calculate the derivative. 
F(x)=x^sqrtx

anonymous · Answer

$$x ^{\sqrt{x}}$$

anonymous · Answer

Take the natural log of both sides, then take the derivative. You will need to use implicit differentiation. Please let me know if you need help with these steps.

anonymous · Answer

i took the natural log and got lny=ln $$x ^{\sqrt{x}}$$

anonymous · Answer

i just need help to solve implicit differentiation

anonymous · Answer

Remember when taking the natural log of something you can bring the exponent down to outside the log. So ln x^(root x) becomes (root x) ln x

anonymous · Answer

oh ok and you solve that using implicit differentiation

anonymous · Answer

Proceed to take the derivative of both sides. (1/y)(dy/dx)= (1/2)x^(-.5)*ln x + (1/2)(root x)

Move the y over, substitue y back in, and you have your derivative.

anonymous · Answer

where did the 1/2 come from after the addition sign?

anonymous · Answer

It should be 1/x of course, but the method is correct. I get:
$$F'(x)=x^{\sqrt{x}-1/2}(\frac{1}{2}lnx+1)$$