Partial Derivative of w Relative to x

golriz
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Hello
I have a question:
Let w=2cot x +y^2.z^2
x = uv
y = sin(uv)
z = e^v
Find the partial derivative of w releative to x.
 
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Treat y^2.z^2 as a constant and derive with respect to x (the y^2.z^2 term will disappear). If you need any more help please post what you tried to do :).

PS. Partial derivatives aren't really pre-calculus :P
 
That's a pretty straight forward problem. You may be thinking it is harder than it is because, since u, v, and w are not present in the problem, the information you give: x=uv, y= sin(uv), z= ev is irrelvant. Please show us what you have done. In particular, what is the derivative of tan(x)?

As focus said, this is not at all "precalculus". I am going to move this to the "calculus and beyond" homework area.
 
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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