First Derivative of (5/x)+(5/SQRT(x)): Homework Equations & Rules to Solve

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Homework Statement


Find the first derivative of (5/x)+(5/SQRT(x))


Homework Equations



Derivative ruls

The Attempt at a Solution


attachment.php?attachmentid=53629&stc=1&d=1354648651.jpg


Is this correct? Thank you
 

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Yes.
 
Thank you
 
Unless this problem requires the use of the quotient rule, it can be done much more simply using the power rule.

$$\frac{d}{dx}\left(\frac{5}{x} + \frac{5}{\sqrt{x}} \right)$$
= d/dx(5x-1 + 5x-1/2)
= -5x-2 - (1/2)x-3/2
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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