+0  
 
0
888
2
avatar

how do you do the derivative of 6.687(.931)^x?

Guest Apr 16, 2015

Best Answer 

 #2
avatar+90988 
+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
Sort: 

2+0 Answers

 #1
avatar+78577 
+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
avatar+90988 
+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

15 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details