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Checkfate
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I need help differentiating [tex] y=\sqrt{x-2}\sqrt{x+1} [/tex]
I am using a mix of the chain rule and product rule which my textbook for school wants me to use for this. So suggestions for different ways of approaching it won't help :P Anyways, thanks in advance for looking over it. It's my first attempt at posting in latex so let's hope it works!
For my work I have:
(dy)/(dx)=[tex](x-2)^{1/2}\frac{d}{dx}(x+1)^{1/2}+(x+1)^{1/2}\frac{d}{dx}(x-2)^{1/2}[/tex]
=[tex](x-2)^{1/2}(\frac{1}{2})(x+1)^{-1/2}+(x+1)^{1/2}(\frac{1}{2})(x-2)^{-1/2}[/tex]
And that is exactly what they have in my textbook, so that's good. But...
For the third part my textbook has
=[tex](\frac{1}{2})(x+1)^{-1/2}(x-2)^{\frac{-1}{2}}(x-2+x+1)[/tex]
This is the step that I am not understanding, it's simple algebra but I am still not quite getting it :( Can someone help?
Then the last step is
=[tex] \frac{2x-1}{2(x+1)^{1/2}(x-2)^{1/2}}[/tex] Which I somewhat understand, but not really.
\
PS - For the third step I am getting
=[tex](x-2)^{1/2}(\frac{1}{2})(x+1)^{-1/2}+(\frac{1}{2})(x+1)^{1/2}(x-2)^{-1/2} [/tex]
I am using a mix of the chain rule and product rule which my textbook for school wants me to use for this. So suggestions for different ways of approaching it won't help :P Anyways, thanks in advance for looking over it. It's my first attempt at posting in latex so let's hope it works!
For my work I have:
(dy)/(dx)=[tex](x-2)^{1/2}\frac{d}{dx}(x+1)^{1/2}+(x+1)^{1/2}\frac{d}{dx}(x-2)^{1/2}[/tex]
=[tex](x-2)^{1/2}(\frac{1}{2})(x+1)^{-1/2}+(x+1)^{1/2}(\frac{1}{2})(x-2)^{-1/2}[/tex]
And that is exactly what they have in my textbook, so that's good. But...
For the third part my textbook has
=[tex](\frac{1}{2})(x+1)^{-1/2}(x-2)^{\frac{-1}{2}}(x-2+x+1)[/tex]
This is the step that I am not understanding, it's simple algebra but I am still not quite getting it :( Can someone help?
Then the last step is
=[tex] \frac{2x-1}{2(x+1)^{1/2}(x-2)^{1/2}}[/tex] Which I somewhat understand, but not really.
\
PS - For the third step I am getting
=[tex](x-2)^{1/2}(\frac{1}{2})(x+1)^{-1/2}+(\frac{1}{2})(x+1)^{1/2}(x-2)^{-1/2} [/tex]
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