Differentiation

[StintedVisions]

I need to take the derivative of x(36-x^2)^1/2

I guess I missed a step considering my answer was slightly off from what the actual answer was. I got
f'(x)=x(1/2(36-x²)^-1/2(-2x)
=-2x²/2(36-x²)^1/2
=-x²/(36-x²)^1/2

Where am I going wrong?

 

[mathmari]

(x(36-x²)^1/2)'=(x)'(36-x²)^1/2+x((36-x²)^1/2)'=(36-x²)^1/2+x(1/2)*(36-x²)^-1/2(-2x)=(36-x²-x²)/(36-x²)^1/2=(36-2x²)/(36-x²)^1/2

 

[StintedVisions]

Right, the product rule....
Thank you.