Simplify Derivative of log(x^2 + y^2) - z^3

mill
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Homework Statement



Simplify ##d(log(x^2 + y^2) − z^3)##

Homework Equations



the derivative?

The Attempt at a Solution



The instruction says to simplify. In a similar problem I ended up using the d(a(b-c))= da d(b-c). I am not sure how to deal with the log and only found formulas for ln. Could I just substitute the whole log term with another variable?
 
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mill said:

Homework Statement



Simplify ##d(log(x^2 + y^2) − z^3)##

Homework Equations



the derivative?

The Attempt at a Solution



The instruction says to simplify. In a similar problem I ended up using the d(a(b-c))= da d(b-c). I am not sure how to deal with the log and only found formulas for ln. Could I just substitute the whole log term with another variable?
d is not the derivative. Its a variable there.
 
adjacent said:
d is not the derivative. Its a variable there.

The instruction says to simplify the differential. So I assumed it was the derivative?
 
The differential of a function of more variables ##df(x,y,z) =\frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy+\frac{\partial f}{\partial z}dz.##

Now ##f(x,y,z) = log(x^2 + y^2) − z^3##. Take the partial derivatives and write up the differential.

ehild
 

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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