# Thread: How do you differentiate this function?!?

1. ## How do you differentiate this function?!?

f(x,y)= e^ax loge(y)

I need to find the first order, second order and cross partial derivatives of this function. I have some answers that a friend has given me but I have no idea how they've been calculate what techniques/rules have been employed so any help/explanation would be greatly appreciated. Cheers!

2. ## Re: How do you differentiate this function?!?

Originally Posted by AEJD90
f(x,y)= e^ax loge(y)

I need to find the first order, second order and cross partial derivatives of this function. I have some answers that a friend has given me but I have no idea how they've been calculate what techniques/rules have been employed so any help/explanation would be greatly appreciated. Cheers!
A general rule of thumb is that when performing a partial derivative, treat every variable except the variable being differentiated with respect to, as fixed or constant. The same derivative rules (such as the product, chain and quotient rules) still apply.

3. ## Re: How do you differentiate this function?!?

First, the standard notation for "loge(y)" is ln(y). Do you know the derivative of ln(y) with respect to y? Do you know the derivative of $e^{ax}$ with respect to x? As ProveIt said, to differentiate with respect to x, treat y as a constant, and to differentiate with respect to y, treat x as a constant. Here, you just have a function of x times a function of y: F(x, y)= f(x)g(y).

So $F_x= f_x(x)g(y)$, $F_y= f(x)g_y(y)$, $F_{xx}= f_{xx}(x)g(y)$, $F_{yy}= f(x)g_{yy}(y)$, and $F_{xy}= F_{yx}= f_x(x)g_y(y)$.