Thread: Help with the quotient rule of derivatives, involving negative exponents.

So basically the function is: f(x) = x² (x² + 1)^-3.

I have to use the quotient rule to differentiate it. I just started derivatives, so I don't quite understand it. I've had like 5 different tutors or people explain this specific problem, but I still don't understand it and they all got frustrated with me when I didn't understand.

I understand d/dx (u/v) = (v (du/dx) - u (dv/dx)) / (v2) is the quotient rule. I understand this no problem.

u = x² v = (x² + 1)³

f(x) = (x²)/(x²+1)³

= ((x² + 1)³ (2x) - (x²) 3(x² + 1)² (2x))/(x² + 1)⁶ I understand this because it's just using the quotient rule and deriving what you can in there.

= ((x² + 1)³ (2x) -6x³ (x² + 1)²) / (x² + 1)⁶ This is just simplifying, so I understand this....

Then after there is where the tutors lose me, I've had the tutors come to different answers too, so I have no idea, super frustrated.

Originally Posted by bnosam

So basically the function is: f(x) = x² (x² + 1)^-3.

I have to use the quotient rule to differentiate it. I just started derivatives, so I don't quite understand it. I've had like 5 different tutors or people explain this specific problem, but I still don't understand it and they all got frustrated with me when I didn't understand.

I understand d/dx (u/v) = (v (du/dx) - u (dv/dx)) / (v2) is the quotient rule. I understand this no problem.

u = x² v = (x² + 1)³

f(x) = (x²)/(x²+1)³

= ((x² + 1)³ (2x) - (x²) 3(x² + 1)² (2x))/(x² + 1)⁶ I understand this because it's just using the quotient rule and deriving what you can in there.

= ((x² + 1)³ (2x) -6x³ (x² + 1)²) / (x² + 1)⁶ This is just simplifying, so I understand this....

Then after there is where the tutors lose me, I've had the tutors come to different answers too, so I have no idea, super frustrated.

What you have is correct. If you want, you can take out a common factor of and cancel it, and then simplify whatever is left...

Originally Posted by Prove It

What you have is correct. If you want, you can take out a common factor of and cancel it, and then simplify whatever is left...

Yeah, I was over thinking it...silly silly silly. Thanks, though!