Question

How do you find the derivative of X^2/X^2+4? I don't understand what you have to do to find the derivative.

Answer 1

\[x ^{2}/x ^{2}+4\]

Answer 2

Since it is a quotient you use the quotient rule.

Answer 3

\[(\frac{u(x)}{v(x)})'=\frac{u'(x) \cdot v(x) - v'(x) \cdot u(x) }{u^2(x)}\]

Answer 4

\[h(x)=\frac{u(x)}{v(x)}=\frac{x^2}{x^2+4} => u(x)=x^2 \text{ and } v(x)=x^2+4\]

Answer 5

So what is u'(x) and v'(x) equal to?

Answer 6

0?

Answer 7

Neither u or v are constant functions so no the derivative is not 0.

Answer 8

\[\text{ power rule -> } (x^n)'=nx^{n-1} \]
\[\text{ constant rule -> Let c be a constant } (c)'=0\]

Answer 9

\[\text{ if } u(x)=x^2 \text{ then } u'(x)=(x^2)'=? \]
\[if v(x)=x^2+1 \text{ then } v'(x)=(x^2+1)'=?\]
Write in what the question mark should be for each statement.