Find the derivative and simplify dy/dx if y(x)=square root x^2 +6 Sorry, I am not sure how to make a square root symbol over the x^2+6 on here.

Question

Find the derivative and simplify dy/dx if y(x)=square root x^2 +6     Sorry, I am not sure how to make a square root symbol over the x^2+6 on here.

anonymous · Answer

Let $f(x)=\sqrt{x^2+6}$. Then$$f'(x)=\frac{2x}{2\sqrt{x^2+6}}.$$

anonymous · Answer

Simplify it.

anonymous · Answer

Are you interested in knowing how I got that or did you just want an answer?

anonymous · Answer

x/squareroot x^2+6  this would be simplified right?

anonymous · Answer

Yes

anonymous · Answer

just a question - how can it be simplified with radical in the denominator?

anonymous · Answer

It's called "rationalizing" the function. Basically,$$f'(x)=\frac{x}{\sqrt{x^2+6}}=\frac{x\sqrt{x^2+6}}{x^2+6}.$$

anonymous · Answer

I thought your answer was going to leave the sq rt in the denominator.  I understand rationalizing and was just ensuring that in order to be considered simplified that you still had to do that.

anonymous · Answer

Some people don't consider rationalizing the function as simplifying it.