# Partial differentiation

#### cabellos

Iv forgotten the basics of this. How do we go about differentiating 3x^2 y^2 w.r.t y? I know the answer is 3x^2 y^2 but could someone explain this for me please?

#### cristo

Staff Emeritus
Iv forgotten the basics of this. How do we go about differentiating 3x^2 y^2 w.r.t y? I know the answer is 3x^2 y^2 but could someone explain this for me please?
You want to perform $$\frac{\partial}{\partial y}(3x^2y^2)$$.

You would simply treat the function of x as a constant and differentiate y normally, thus yielding $6x^2y$.

However, this is not what your answer is, so I wonder whether it is the correct question?

#### cabellos

ooops im getting myself all confused now. I know how to do partial differentiation after all. I was reading the wrong solution as the question was z = x^2 y^2 and ofcourse dz/dy would = 3x^2 y^2 !!

#### cristo

Staff Emeritus
ooops im getting myself all confused now. I know how to do partial differentiation after all. I was reading the wrong solution as the question was z = x^2 y^2 and ofcourse dz/dy would = 3x^2 y^2 !!
Erm.. no it wouldn't.

Unless you mean z=x2y3, in which case, dz/dy would be the answer you quoted.

#### cabellos

i need some sleep!! Yeah i meant y^3 lol !

#### Gib Z

Homework Helper
Its a big warning flag when the derivative is equal to the original function and doesn't involve e in it....

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