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Calculus Equation Check

Kris

New member
May 22, 2013
29
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
 
Last edited:

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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?
 

Kris

New member
May 22, 2013
29
Hi Mark,

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

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Hi Mark,

I realised 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?
 

Kris

New member
May 22, 2013
29
Yes that is what I meant
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Okay, good! :D

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