Find the derivative of the fcn:
$$\sqrt{2x + \sqrt{2x + \sqrt{2x}} }$$

Attempt:
Is this the same as:
$$(2x + (2x + (2x)^{1/2})^{1/2})^{1/2}$$
?

Question

Find the derivative of the fcn:
$$\sqrt{2x + \sqrt{2x + \sqrt{2x}} }$$

Attempt:
Is this the same as:
$$(2x + (2x + (2x)^{1/2})^{1/2})^{1/2}$$
?

anonymous · Answer

yes

anonymous · Answer

Yes, you are going to use the chain rule, three times, in order to find this derivative.

anonymous · Answer

Ok Let me show you what I got. One minute, please get back to me soon.

anonymous · Answer

Ok here it is:

anonymous · Answer

$$f'(x) = 1/2(2x(2x + (2x)^{1/2})^{1/2})^{-1/2} * x(2x + (2x)^{1/2})^{-1/2}*(2 + x^{-1/2}) $$

anonymous · Answer

Here is what I got:
$$f \prime(x)=\left[ 2x+(2x+(2x)^{1/2} \right]^{-1/2}\left[ 2+1/2(2x+(2x)^{1/2})^{-1/2} \right]\left[ 2+(2x)^{-1/2} \right]$$

anonymous · Answer

That was lengthy, and labrynthine!