1. ## Differentiation - Basics

Hi,
I am trying to differentiate $\displaystyle e^{-3x}$.

I don't understand why this is the correct answer: $\displaystyle -3e^{-3x}$

Shouldn't the answer be this: $\displaystyle -3e^{-3x-1}$ ?

My understanding of differentiation is that if $\displaystyle y = ax^b$, then $\displaystyle y' = b \cdot ax^{b-1}$

2. Originally Posted by sparky
Hi,
I am trying to differentiate $\displaystyle e^{-3x}$.

I don't understand why this is the correct answer: $\displaystyle -3e^{-3x}$

Shouldn't the answer be this: $\displaystyle -3e^{-3x-1}$ ?

My understanding of differentiation is that if $\displaystyle y = ax^b$, then $\displaystyle y' = b \cdot ax^{b-1}$
the power rule for derivatives only works for constant exponents

for constant $\displaystyle n$ ...

$\displaystyle \dfrac{d}{dx} x^n = nx^{n-1}$

for $\displaystyle u$ a function of $\displaystyle x$ ...

$\displaystyle \dfrac{d}{dx} e^u = e^u \cdot \dfrac{du}{dx}$

3. Originally Posted by skeeter
the power rule for derivatives only works for constant exponents

for constant $\displaystyle n$ ...

$\displaystyle \dfrac{d}{dx} x^n = nx^{n-1}$

for $\displaystyle u$ a function of $\displaystyle x$ ...

$\displaystyle \dfrac{d}{dx} e^u = e^u \cdot \dfrac{du}{dx}$
Thanks skeeter. I understand now.