Partial Derivative of y with Respect to d: Δy

lemaire
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Homework Statement



I have an initial data of d= 0.012608, V = 320 volt, Q = 1.50e-8 and A = 1.25e-4. y = Qd/AV. what is Δy , the partial derivative of y with respect to d?

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The Attempt at a Solution

 
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When you take the partial derivative with respect to a variable, you treat all other variables as constants, so what is

\frac{\partial}{\partial d} \left( \frac{Q}{AV} d \right)

when you treat \frac{Q}{AV} as a constant?
 

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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