# Second derivative of an exponential function

1. Jul 22, 2013

### Calculus :(

1. The problem statement, all variables and given/known data
I have the derived function:
f'(x) = [1/(1+kx)^2]e^[x/(1+kx)]
k is a positive constant

2. Relevant equations
I need to find the second derivative, which I thought was just the derivative of the exponent multiplied by the coefficient (as you find the first derivative), but the answers say:

f''(x) = [1/(1+kx)^4]e^[x/(1+kx)] + e^[x/(1+kx)] . [-2k/(1+kx)^3]

3. The attempt at a solution
All I managed to get was:
f''(x) = [1/(1+kx)^4]e^[x/(1+kx)]
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 22, 2013

### Ray Vickson

You say "I thought was just the derivative of the exponent multiplied by the coefficient (as you find the first derivative)...", but THAT is not true: it is true ONLY if the "coefficient" of the exponential is a constant. If the coefficient itself is a function of x it will not work. Go back and review some basic properties of derivatives.

3. Jul 22, 2013

### Mandelbroth

$\frac{df}{dx}=\frac{e^{\frac{x}{1+kx}}}{(1+kx)^2}$. You have the quotient of two functions of $x$. You can't just take the derivative of the exponential term. What do you do when you have a product or quotient of functions?