Question:
How do you turn 1/2(72+x^2)^(-1/2) into x/sqrt(72+x^2)?
I get that you flip it, but what happens to the 2nd 1/2 and where does the x in the numerator come from?

Question

Question:
How do you turn 1/2(72+x^2)^(-1/2) into x/sqrt(72+x^2)?
I get that you flip it, but what happens to the 2nd 1/2 and where does the x in the numerator come from?

anonymous · Answer

are you taking a derivative?  because other wise it is not the same

anonymous · Answer

ok let start from the beginning

anonymous · Answer

f(x)=sqrt(72+x^2)

= (72+x^2)^(1/2)

f'(x)=1/2 (72+x^2)^(-1/2) * (2x)

=x / sqrt(72+x^2)

f'(7)=7/sqrt(72+49)

=7 / sqrt(121)

=7 / 11

anonymous · Answer

@satellite73

anonymous · Answer

f'(x)=1/2 (72+x^2)^(-1/2) * (2x)

=x / sqrt(72+x^2)

this is the step im asking about

.sam. · Answer

you were trying to find the derivative of f(x)=sqrt(72+x^2)?

anonymous · Answer

yes. i just wanna know about that step. everything else makes sense to me and is correct.

.sam. · Answer

$$y=\sqrt{72+x ^{2}}$$
$$y=(72+x^2)^{1/2}$$
Chain rule,
$$y'=(1/2)(72+x^2)^{-1/2}(2x)$$
$$y'=\frac{1}{2}\frac{2x}{\sqrt{72+x ^{2}}}$$
$$y'=\frac{x}{\sqrt{72+x ^{2}}}$$

.sam. · Answer

you dont understand the chain rule?

anonymous · Answer

i just dont like the flipping part

anonymous · Answer

confuses me sometimes

.sam. · Answer

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