CatchThis2
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Find the partial derivative indicated. Assume the variables are restricted to a domain on which the function is defined.
Partial Derivative
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CatchThis2 said:
Assume that "M" is the only independant variable.
Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.
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My first question would if r and G are independent of M?
If so, \(\displaystyle \frac{\partial}{\partial M}\frac{4\pi r^\frac{7}{2}}{\sqrt{G\cdot M}} = \frac{\partial}{\partial M}\frac{4\pi r^\frac{7}{2}}{\sqrt{G}}\cdot \frac{1}{\sqrt{M}} = \frac{4\pi r^\frac{7}{2}}{\sqrt{G}}\cdot \frac{\partial}{\partial M}\frac{1}{\sqrt{M}}\)
If so, \(\displaystyle \frac{\partial}{\partial M}\frac{4\pi r^\frac{7}{2}}{\sqrt{G\cdot M}} = \frac{\partial}{\partial M}\frac{4\pi r^\frac{7}{2}}{\sqrt{G}}\cdot \frac{1}{\sqrt{M}} = \frac{4\pi r^\frac{7}{2}}{\sqrt{G}}\cdot \frac{\partial}{\partial M}\frac{1}{\sqrt{M}}\)