# Math Help - Differentiation

1. ## Differentiation

Kindly help me with the following question.

1. Consider the functional equation f(x-y)=f(x)/f(y). If f'(0)=p and f'(5)=q, then f'(-5) is
A. p^2/q B. q/p C.p/q D. q

I tried differentiating the function but then I would have dy/dx in the function which I do not know how to eliminate.

2. Originally Posted by champrock
Kindly help me with the following question.

1. Consider the functional equation f(x-y)=f(x)/f(y). If f'(0)=p and f'(5)=q, then f'(-5) is
A. p^2/q B. q/p C.p/q D. q

I tried differentiating the function but then I would have dy/dx in the function which I do not know how to eliminate.
In the equation f(x-y)=f(x)/f(y) there are two independent variables, x and y. It does not make sense to talk about dy/dx because x and y are independent of each other.

What you need to do is to differentiate partially with respect to x and y. If you differentiate partially with respect to x then you find that $f'(x-y) = \frac{f'(x)}{f(y)}$. If you differentiate partially with respect to y then you find that $-f'(x-y) = -\frac{f(x)}{(f(y))^2}f'(y)$. That gives you enough information to solve the problem.

3. Thanks a lot!!