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

[mill]

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?

 

[adjacent]

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.

 

[mill]

d is not the derivative. Its a variable there.

The instruction says to simplify the differential. So I assumed it was the derivative?

 

[ehild]

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