Will someone prove this derivative

http://25.media.tumblr.com/tumblr_mc3yyi…

I don't understand why there's a negative x on top. I thought it should be a negative 1.

When you do the chain rule, the derivative of the "inside" is -2x, so that goes in the numerator. And when you do the derivative of the "outside," you get a 1/(2sqrt(100-x^2)) (multiply by the exponent, which is 1/2, and then decrease it by 1 to get a new exponent of -1/2).

Then you have a 2 in both the numerator and denominator, so they cancel, leaving -x in the numerator.

Hey Joey

Nice Youtube piano piece. Let's do some calculus, shall we? Ok. The problem is, what is the derivative of y = √(100 - x²), right? Let's go!

y = √(100 - x²)             given
y = (100 - x²)¹ˡ²             rewrite

Let u = 100 - x². We now have:

y = u¹ˡ²
dy/du = ½u⁻¹ˡ²
du/dx = -2x

dy/dx = dy/du·du/dx

dy/dx = (½u⁻¹ˡ²) · (-2x)
dy/dx = -2x/2·u⁻¹ˡ²
dy/dx = -x/√(100 - x²)

I got the answer pictured in the link you provided. I hope you can follow the chain-rule application.

Good luck!
alice

y = sqrt(100-x^2)
y = (100-x^2)^(1/2)
now use the chain rule
y' = (1/2)(100-x^2)^(-1/2)(-2x) remember you reduce the exponent by 1 when you differentiate
y' = -x/sqrt(100-x^2)