# Differentiation - Basics

• Mar 9th 2011, 03:59 PM
sparky
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 $\displaystyle y' = b \cdot ax^{b-1}$
• Mar 9th 2011, 04:21 PM
skeeter
Quote:

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 $\displaystyle x$ ...

$\displaystyle \dfrac{d}{dx} e^u = e^u \cdot \dfrac{du}{dx}$
• Mar 9th 2011, 04:47 PM
sparky
Quote:

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.