Differentiation

Question

Given that y= x√(3-x²) , show that dy/dx = (3+2x²) / (√3+x² ) .

 

Is it possible to get a positive x value? My answer is (3-2x2) / √(3-x2 ) .

 

 

 

 

 

Thank You!

Answer 1

 

Since √(3-x²) calls for use of the Chain Rule, let u = (3-x²). du/dx = -2x

 

Rewrite the original equation as y = x √(u).  -2y = = -2x √u  so we have -2y = (u)^1/2 du/dx.

 

-2 dy/dx = (1/2)*u^(-1/2).   dy/dx  = (-1/4)*u^(-1/2).

 

Now move u to the denominator and replace u:  dy/dx = (-1) / 4√(3-x²)