How do you differentiate sqrt(16-x^2)16x2?

1 Answer
Nov 12, 2016

d/dxsqrt(16-x^2)=-1/sqrt(16-x^2)ddx16x2=116x2

Explanation:

diff'n of sqrt(x)x is d/dxx^(1/2)ddxx12
apply n-1n1 rule: 1/2x^(1/2-1)\rightarrow1/2x^(-1/2)12x12112x12

therefore...
d/dxsqrt(16-x^2)ddx16x2

apply chain rule
1/2(16-x^2)^(-1/2)\timesd/dx(16-x^2)12(16x2)12×ddx(16x2)

differentiate
(1/(2\times(16-x^2)^(1/2)))\times-2x(12×(16x2)12)×2x

simplify:
-1/sqrt(16-x^2)116x2