# Basic partial derivative question

• Jan 10th 2010, 09:33 PM
alekb
Basic partial derivative question
I am reviewing some concepts and I do not remember the proper way solve this problem.
I need to differentiate f with respect to x and with respect to y (partial derivatives) for:
f(x,y) = ln(x^5+xy+(y^3)(e^x))
My guess is that f with respect to x is:

(5x^4+y+(y^3)(e^x))((1/ (x^5+xy+(y^3)(e^x)))
But I am pretty sure that my guess is not correct. Can anyone help me with this, please?
• Jan 10th 2010, 09:49 PM
Drexel28
Quote:

Originally Posted by alekb
I am reviewing some concepts and I do not remember the proper way solve this problem.
I need to differentiate f with respect to x and with respect to y (partial derivatives) for:
f(x,y) = ln(x^5+xy+(y^3)(e^x))
My guess is that f with respect to x is:

(5x^4+y+(y^3)(e^x))((1/ (x^5+xy+(y^3)(e^x)))
But I am pretty sure that my guess is not correct. Can anyone help me with this, please?

You tell us. $\frac{\partial}{\partial x}f(x,y)$ is just like considering $f(x,y)$ as a function of $x$ and treating $y$ as constant.
• Jan 10th 2010, 10:15 PM
you can see the attachment for the answer

the mistake you were making is for the implicit differentiation part

for example IF you have to differentiate f(x) = xy

then you use product rule = derivative of the first times the second + the derivative of the second times the first = 1y + y'x when you differentiate y then you get y'

Second example f(x)= (x^3)(y^3) = 3(x^2)(y^3) + 3(y^2)y'(x^3)

you can review implicit differentiation from youtube
• Jan 10th 2010, 10:44 PM
alekb
I thought that I did not need to add the y part of it while differentiating for x.

I know that the derivative of ln(x) is 1/x, based on that assumption I solved ln(x^5+xy+(y^3)(e^x)) as 1/(x^5+xy+(y^3)(e^x)).

My problem is that I do not know how to link the derivative of the part inside the brackets with the derivative of ln(x).

Because I am treating y as a constant, I took the derivative of the part inside the brackets and connected it with the derivative of ln(x); however I do not know if I am supposed to do this:

((1/ (x^5+xy+(y^3)(e^x)))(5x^4+y+(y^3)(e^x))
• Jan 15th 2010, 10:11 AM