# Finding Derivatives of Functions

• July 13th 2011, 05:32 AM
StarDancer19
Finding Derivatives of Functions
I am working on some homework and am stuck when it comes to problems like these:

Find ds/dt if s=ln[t^8(t^7-2)]

Thanks for the help!
• July 13th 2011, 05:42 AM
Siron
Re: Finding Derivatives of Functions
Where is the problem? Do you know the derivative of ln(u) where u is a function? ...
You have to use the 'chain rule'.
• July 13th 2011, 05:52 AM
StarDancer19
Re: Finding Derivatives of Functions
I think that u= t^7-2 so therefore the derivative would be 7t^6
• July 13th 2011, 05:56 AM
Re: Finding Derivatives of Functions
Quote:

Originally Posted by StarDancer19
I am working on some homework and am stuck when it comes to problems like these:

Find ds/dt if s=ln[t^8(t^7-2)]

Thanks for the help!

One way is to use $ln(ab)=lna+lnb$

$\frac{d}{dt}ln\left[t^8\left(t^7-2\right)\right]=\frac{d}{dt}lnt^8+\frac{d}{dt}ln\left(t^7-2\right)$

$x=t^8,\;\;y=t^7-2$

$\frac{ds}{dt}=\frac{d}{dt}lnx+\frac{d}{dt}lny$

$=\frac{dx}{dt}\;\frac{d}{dx}lnx+\frac{dy}{dt}\; \frac{d}{dy}lny$

You could also first evaluate $t^8\left(t^7-2\right)=t^{15}-2t^8$
and work from there.
• July 13th 2011, 05:56 AM
Siron
Re: Finding Derivatives of Functions
Why not: u=t^8(t^7-2)=t^15-2t^8?
You know:
D(ln(u))=D(u)/u

Can you finish it? ...
• July 13th 2011, 06:28 AM
StarDancer19
Re: Finding Derivatives of Functions
Yeah, I guess that the t^8 would also be apart of the u. But no, I'm still confused on how to finish it.
• July 13th 2011, 06:31 AM
Siron
Re: Finding Derivatives of Functions