Need help finding the derivative(not a difficult problem)

Limits, differentiation, related rates, integration, trig integrals, etc.
mike09
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Need help finding the derivative(not a difficult problem)

Postby mike09 » Mon Oct 15, 2012 9:40 pm

Hi, I know the following question isn't too difficult; I just need some clarification.

Find the derivative of the function:

f(x)= 3(x^5 + x)^6

would the answer to that problem be 18(x^5 + x)^5?

whereas if the problem were f(x)=3x(x^5 +x)^6 you would have to use the product rule followed by the chain rule correct?

Thanks in advance

nona.m.nona
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Re: Need help finding the derivative(not a difficult problem

Postby nona.m.nona » Mon Oct 15, 2012 11:34 pm

mike09 wrote:Find the derivative of the function:

f(x)= 3(x^5 + x)^6

would the answer to that problem be 18(x^5 + x)^5?

No. You have differentiated the outer process, being the "raised to the sixth power". You now need to differentiate the inner process, being the polynomial. In other words, you need to apply the Chain Rule to complete this differentiation.

mike09 wrote:whereas if the problem were f(x)=3x(x^5 +x)^6 you would have to use the product rule followed by the chain rule correct?

This would involve both the Product Rule and the Chain Rule, yes.

mike09
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Joined: Mon Oct 15, 2012 9:32 pm
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Re: Need help finding the derivative(not a difficult problem

Postby mike09 » Mon Oct 15, 2012 11:52 pm

nona.m.nona wrote:
mike09 wrote:Find the derivative of the function:

f(x)= 3(x^5 + x)^6

would the answer to that problem be 18(x^5 + x)^5?

No. You have differentiated the outer process, being the "raised to the sixth power". You now need to differentiate the inner process, being the polynomial. In other words, you need to apply the Chain Rule to complete this differentiation.

mike09 wrote:whereas if the problem were f(x)=3x(x^5 +x)^6 you would have to use the product rule followed by the chain rule correct?

This would involve both the Product Rule and the Chain Rule, yes.


Thank you so much for helping me out.....now that I applied the chain rule to the polynomial would the answer be 18(x^5 + x)^5(5x^4 + 1)?

nona.m.nona
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Joined: Sun Dec 14, 2008 11:07 pm
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Re: Need help finding the derivative(not a difficult problem

Postby nona.m.nona » Tue Oct 16, 2012 1:03 am

mike09 wrote:would the answer be 18(x^5 + x)^5(5x^4 + 1)?

Yes.


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