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.

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.

anonymous · Answer

$$x ^{2}/x ^{2}+4$$

myininaya · Answer

Since it is a quotient you use the quotient rule.

myininaya · Answer

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

myininaya · Answer

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

myininaya · Answer

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

anonymous · Answer

0?

myininaya · Answer

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

myininaya · Answer

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

myininaya · Answer

$$\text{ if } u(x)=x^2  \text{ then } u'(x)=(x^2)'=? $$
$$if v(x)=x^2+1 \text{ then } v'(x)=(x^2+1)'=?$$
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