Need help finding the derivative(not a difficult problem)

[mike09]

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]

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.

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]

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.

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]

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

Yes.