Problems 1F-7 and 1F-8.
Ex. 1F-7 a) D = srt( (x-a)^2 +y0^2 ) Find dD/dx

My answer: 1/2( (x-a)^2 + y0^2) )^-1/2 (2(x-a) + 2y(dy/dx))

Correct answer: 1/2( (x-a)^2 + y0^2) )^-1/2 (2(x-a))

My question: what happened to the y derivative? Why is there no 2y(dy/dx)? How does this relate to the fact that we're not looking for dy, but we are looking for dD? (I have the same problem for the rest of the problems in part 1F-7 and 1f-8). Thanks!

Question

Problems 1F-7 and 1F-8. 
Ex. 1F-7 a) D = srt( (x-a)^2 +y0^2 ) Find dD/dx

My answer: 1/2( (x-a)^2 + y0^2) )^-1/2 (2(x-a) + 2y(dy/dx))

Correct answer: 1/2( (x-a)^2 + y0^2) )^-1/2 (2(x-a))

My question: what happened to the y derivative? Why is there no 2y(dy/dx)? How does this relate to the fact that we're not looking for dy, but we are looking for dD? (I have the same problem for the rest of the problems in part 1F-7 and 1f-8). Thanks!

anonymous · Answer

Well, it is given 'y0^2' (NOT just y). The y0 is a constant, it seems. So on differention of the constant y0, it results to 0.

jkristia · Answer

kutabs is correct.
You are finding the derivative of $\frac{dD}{dx}$, so you are finding the derivative of D with respect to x, and $y_{0}$ is just a constant