# Thread: Basic partial derivative question

1. ## 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?

2. 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. $\displaystyle \frac{\partial}{\partial x}f(x,y)$ is just like considering $\displaystyle f(x,y)$ as a function of $\displaystyle x$ and treating $\displaystyle y$ as constant.

3. 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

4. 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))

5. Sorry about the wrong information. I have not learned partial derivatives yet in Calculus. I just looked it up on Google and you are right about treating y as a constant. I thought you were talking about implicit differentiation. I am sorry for the misunderstanding.