#2**+5 **

$$\boxed{If\;\;y=a^x\;\;then\;\;\frac{dy}{dx}=(lna)a^x}$$

Mmm, I didn't know this short cut Chris, I will have to try and remember it! Wish me luck. :)

This is how I would have done it,

$$\\y=6.687*0.9316^x\\\\

\frac{y}{6.687}=0.9316^x\\\\

ln(\frac{y}{6.687})=ln(0.9316^x)\\\\

ln(y)-ln(6.6870)=xln(0.9316)\\\\

\frac{1}{y}\;\frac{dy}{dx}-0=ln(0.9316)\\\\

\frac{dy}{dx}=yln(0.9316)\\\\

$sub in y$\\\\

\frac{dy}{dx}=6.687*0.9316^x*ln(0.9316)\\\\

\frac{dy}{dx}=6.687*ln(0.9316)*0.9316^x\\\\$$

Melody
Apr 17, 2015

#1**+5 **

The derivative of a^x = ln(a) * a^x

So, the derivative of (.931)^x = ln(.931) * (.931)^x

You can evaluate ln(.931) on your calculator......then.....multiply that times 6.687 and then "tack" the "(.931)^x " part on at the end.......

CPhill
Apr 16, 2015

#2**+5 **

Best Answer

$$\boxed{If\;\;y=a^x\;\;then\;\;\frac{dy}{dx}=(lna)a^x}$$

Mmm, I didn't know this short cut Chris, I will have to try and remember it! Wish me luck. :)

This is how I would have done it,

$$\\y=6.687*0.9316^x\\\\

\frac{y}{6.687}=0.9316^x\\\\

ln(\frac{y}{6.687})=ln(0.9316^x)\\\\

ln(y)-ln(6.6870)=xln(0.9316)\\\\

\frac{1}{y}\;\frac{dy}{dx}-0=ln(0.9316)\\\\

\frac{dy}{dx}=yln(0.9316)\\\\

$sub in y$\\\\

\frac{dy}{dx}=6.687*0.9316^x*ln(0.9316)\\\\

\frac{dy}{dx}=6.687*ln(0.9316)*0.9316^x\\\\$$

Melody
Apr 17, 2015