d is not the derivative. Its a variable there.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?
adjacent said:d is not the derivative. Its a variable there.
The derivative of log(x^2 + y^2) - z^3 is 2x/(x^2 + y^2) - 3z^2.
To simplify the derivative, you can first expand the log function using the logarithm rule log(ab) = log(a) + log(b). This gives us log(x^2 + y^2) - log(z^3). Then, using the power rule for derivatives, we can find the derivative of each term separately, giving us 2x/(x^2 + y^2) - 3z^2.
Simplifying the derivative allows us to better understand the behavior of the original function. It also makes it easier to use the derivative in further calculations or applications.
No, the derivative of log(x^2 + y^2) - z^3 is already in its simplest form.
The main steps involved in simplifying the derivative are expanding the log function, finding the derivative of each term, and combining like terms.