Differentiation - Basics

**sparky** · March 9th 2011, 03:59 PM

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

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

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

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

**skeeter** · March 9th 2011, 04:21 PM

Originally Posted by sparky

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

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

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

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

the power rule for derivatives only works for constant exponents

for constant $n$ ...

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

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

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

**sparky** · March 9th 2011, 04:47 PM

Originally Posted by skeeter

the power rule for derivatives only works for constant exponents

for constant $n$ ...

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

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

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

Thanks skeeter. I understand now.

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