What is the partial derivative of f(x, y) with respect to x?

[Kris1]

Hi I am trying to find the gradient function of
f(x, y) = 2*y^3+y*x*2+7/2 y^2+x^2

I have worked out the answer to be
d/dx = 2*y^3+2*y*x+7/2*y^2+2*x
d/dy = 6*y^2+x^2+(7/2)*2*y+x^2

Can someone please check this to make sure I have done the partial derivatives correctly as I am unsure if they are right?

EDIT:

Excuse my poor working the correct answer when I resolved is
2*x*y+2*x,6*y^2+x^2+2*y

 

[MarkFL]

Those are not correct...you need to treat the terms involving the other variable as a constant when taking the partial with respect to a variable/ For example, if given:

\(\displaystyle f(x,y)=x^2+xy+y^2\)

then:

\(\displaystyle \frac{\partial f}{\partial x}=2x+y\)

\(\displaystyle \frac{\partial f}{\partial y}=x+2y\)

Do you see how the terms that do not involve the variable with respect to which we are differentiating vanish to zero?

 

[Kris1]

Hi Mark,

I realized my error and corrected it as your post went up. Thanks for the reminder though

 

[MarkFL]

Hi Mark,

I realized my error and corrected it as your post went up. Thanks for the reminder though

Your results are still not quite right. To make sure, I think you mean to state:

\(\displaystyle f(x,y)=2y^3+x^2y+\frac{7}{2}y^2+x^2\)

Is this correct?

 

[Kris1]

Yes that is what I meant

 

[MarkFL]

Okay, good! :D

Now, let's find the partial with respect to $x$ first, treating $y$ as a constant...what do you get?