Question

okay, so i know the quotient rule and chain rule but im confused on when applying it. the question is find the derivative of the function.
y=(x^2+1 / x+2-1)^3

I used chain rule and got
3(x^2+1 / x+2-1)^2 times (2x/2x)

I am then told to use quotient rule. can someone help me step by step please ?!

Answer 1

is this what is in the parens:
\[ \frac{x^2+1}{x+2} -1 \]?

Answer 2

ah im sorry ! the denominator is x^2-1

Answer 3

so the problem is
\[ \frac{x^2+1}{x^2-1} \]?

the rule is bottom * derivative top - top * derivative bottom
all divided by the bottom squared.

the top of the derivative is
\[ (x^2 - 1) (2x) - (x^2+1)(2x) \\
2x^3 -2x - 2x^3 - 2x \\
- 4x
\]
so the answer is
\[ \frac{ -4x}{(x^2-1)^2} \]