Solving with Chain Rule?

[TigerLilly]

Solve using chain rule: (h12 + x2)½ + (h22 + (L-X)2)½

½ (h12 + x2)-½ * 2h1 + 2x + ½ (h22 + (L-X)-½ * 2 h2 + 2 (L-X)
(h1 + x/ h1² + x²) + h2 + (L-X)/(h2² + (L-X)²)


However, I know this cannot be right because the h1 and h2 are not supposed to be in the numerator in the final answer but I have absolutely no idea what I'm doing wrong? Any clarification is appreciated. And please ignore the cross-through line in my final answer, that was an error with the software I was using to type it out.

 

[HallsofIvy]

What you have written makes no sense. "Solve" what? There is no question or problem given. Do you mean "find the derivative"? If so, with respect to what variables? x? And is "X" supposed to be the same as "x"? Does "x2" mean \(\displaystyle x^2\) (use x^2 if you cannot use Latex)? Are there two "h"s, h_1 and h_2 and does "h12" mean (h_1)^2?

If you mean "Find the derivative of \(\displaystyle (h_1^2+ x^2)^{1/2}+ (h_2^2+ (L- x)^2)^{1/2}\), then we have \(\displaystyle \frac{1}{2}(h_1^2+ x^2)^{-1/2}(2x)+ \frac{1}{2}(h_2^2+ (L-x)^2)^{-1/2}(2(L- x))(-1)\).

As long as \(\displaystyle h_1\) and \(\displaystyle h_2\) are NOT functions of x, their derivative with respect to x is 0, not "\(\displaystyle 2h_1\)" or "\(\displaystyle 2h_2\)".