1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Implicit partial derivative

  1. Feb 10, 2015 #1
    1. The problem statement, all variables and given/known data
    Find (∂z/∂x) of 6xyz

    2. Relevant equations

    3. The attempt at a solution
    The correct answer is 6xy(∂z/∂x) but I would like proof of it. I got something different when I tried taking the partial derivative.

    6xyz = 6x(yz) = Multiplication rule for derivatives

    6(∂x/∂x) + y(∂z/∂x)

    What did I do wrong? Thanks
  2. jcsd
  3. Feb 10, 2015 #2


    Staff: Mentor

    Is this the complete problem statement? Generally speaking you don't find "∂z/∂x" of something, and more than you find "dy/dx" of something. You can, however, find the derivative with respect to, say, x of a function (denoted d/dx(f)) or the partial of some function with respect to, say z (denoted ∂/∂x(f).

    The symbols ∂z/∂x and dy/dx represent derivatives, whereas the symbols ∂/∂x and d/dx represent operators that can be applied to functions.

    Please verify that what you're providing is the complete problem statement.
  4. Feb 11, 2015 #3
    The full question is find (∂z/∂x) of x3 + y3 + z3 + 6xyz = 1
    My textbook says the partial derivative is 3x2 + 3z2(∂z/∂x) + 6xy(∂z/∂x) = 0
    I don't get how to take the derivative of the red part.
  5. Feb 11, 2015 #4
    The derivative above is from my textbook's solutions guide.
  6. Feb 11, 2015 #5


    Staff: Mentor

    Corrected to: find (∂z/∂x) of if x3 + y3 + z3 + 6xyz = 1

    It looks to me like there's a mistake in the solution guide.
    ##∂/∂x(x^3) = 3x^2## and ##∂/∂x(y^3) = 0## and ##∂/∂x(z^3) = 3z^2 ∂z/∂x##

    ##∂/∂x(6xyz) = 6yz## if z is independent of x, in which case ∂z/∂x would be 0. However, if z is dependent on x, you need to use the product rule. Since you're asked to find ∂z/∂x, it must be the case that z is a function of x (is dependent on x).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Implicit partial derivative
  1. Implicit Derivation (Replies: 9)