# Thread: Whats an easy way to remember d/dx of b^x and logb^x

1. ## Whats an easy way to remember d/dx of b^x and logb^x

Whats an easy way to remember $\displaystyle \frac{d}{dx}[b^x]$and $\displaystyle \frac{d}{dx} logb ^x$ besides remembering the d/dx formulas for them?

I am in calc 2 and I forgot! We haven't used them yet, thankfully.

2. ## Re: Whats an easy way to remember d/dx of b^x and logb^x

Originally Posted by delgeezee
Whats an easy way to remember $\displaystyle \frac{d}{dx}[b^x]$and $\displaystyle \frac{d}{dx} logb ^x$ besides remembering the d/dx formulas for them?

I am in calc 2 and I forgot! We haven't used them yet, thankfully.
derive them yourself ...

$\displaystyle y = b^x$

$\displaystyle \ln{y} = \ln{b^x}$

$\displaystyle \ln{y} = x\ln{b}$

$\displaystyle \frac{d}{dx} \left(\ln{y} = x\ln{b}\right)$

$\displaystyle \frac{y'}{y} = \ln{b}$

$\displaystyle y' = y \cdot \ln{b}$

$\displaystyle y' = b^x \cdot \ln{b}$

------------------------------------------------

$\displaystyle y = \log_b{x}$

$\displaystyle x = b^y$

$\displaystyle \frac{d}{dx}\left(x = b^y\right)$

$\displaystyle 1 = b^y \cdot \ln{b} \cdot y'$

$\displaystyle 1 = x \cdot \ln{b} \cdot y'$

$\displaystyle y' = \frac{1}{x \cdot \ln{b}}$