I am having trouble with two questions, one is with a quotient rule and the other a product rule I believe. Instructions indicate to compute all first order derivatives of the given function.
Z= xe^xy
Here is what I did: fx= (x)(ye^xy) + (e^xy)(1) Is this correct?
I started using the product rule again for (fy) but then I saw an example in the book where they used the constant multiple rule. Why am I supposed to use this rule and not the product rule? The book shows a similar example and they used the product rule to differentiate fx and used the constant multiple rule to differentiate fy, I would just like to know why this is...
My second set of problems is:
1. 2x+3y / y-x
2. e^2-x / y^2
I know the quotient rule can be used, but I was not sure how to keep y and x as constants. If someone can illustrate the steps involved, Thanks...
I am having trouble on this one: f(x,y)= e^(2-x) / y^2
Here is what I did: fx= (y^2)(1e^2-x) - (e^2-x)(0) / (y^2)^2
I think I have the second term wrong and I am not sure about the 0 term being multiplied, but if we are considering that y is a constant, than it would go to zero, if I'm not mistaken. what am I doing wrong? Thanks...
Yes, I understand now, because y is a constant, it doesn't need to be differentiated, so we just leave it as is and differentiate the numerator. Last question, I promise, what would happen when X is a constant and we have fy? Do we use the quotient rule in this case? The book has the answer as fy= -2e^2-x / y^3 I don't see how this was obtained.