# Math Help - differentiate y=a*exp^(-x/b)+c

1. ## differentiate y=a*exp^(-x/b)+c

I need to find the derivative of the following function......

y=a*(exp^(-x/b))+c

Many thanks

2. Originally Posted by Confused169
I need to find the derivative of the following function......

y=a*(exp^(-x/b))+c

Many thanks
The derivative of $a e^{kx}$ is $k a e^{kx}$. In your problem k = -1/b ......

3. Originally Posted by Confused169
I need to find the derivative of the following function......

y=a*(exp^(-x/b))+c

Many thanks
Alternatively you could go this route

$y=ae^{\frac{-x}{b}}+C$

Disregarding the C as 0 when differentiated we just need to tackle

$y=ae^{\frac{-x}{b}}\Rightarrow\ln(y)=\ln\bigg(ae^{\frac{-x}{b}}\bigg)=\ln(a)-\frac{x}{b}$

so differentinag the left side implicitly and the right side regularly we get

$\frac{y'}{y}=\frac{-1}{b}$

so seeing that y is the original equation we get

$y'=\frac{-a}{b}e^{\frac{-x}{b}}$

4. Cheers guys.... thanks for the speedy reply.