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

**Confused169** · June 3rd 2008, 04:03 AM

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

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

can anyone please help me!

Many thanks

**mr fantastic** · June 3rd 2008, 04:45 AM

Originally Posted by Confused169

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

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

can anyone please help me!

Many thanks

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

**Mathstud28** · June 3rd 2008, 05:29 PM

Originally Posted by Confused169

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

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

can anyone please help me!

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

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

**Confused169** · June 4th 2008, 12:31 AM

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

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