Need help with this derivative?

Question

I've tried this problem like 3 times, but I don't know if I'm doing it right. We're going over the quotient rule, which I understand, but I don't think I'm doing the ln((9x^4)- 3x) part right.

the problem is:

Find the derivative of
f(x)=(5^x)(ln((9x^4)- 3x))

Giulia · Answer

You have to look at this in two steps; product rule and chain rule.

Recall Product Rule: Derivative of the first, times the second plus the derivative of the second times the first.

So, 5((ln(9x^4)-3x)

this is where we use chain rule. Recall, derivative of the outside, time the derivative of the inside.

So, 5^x((ln(9x^4)-3x)   1/(9x^4-3x)((36x^3)-3)(5^x)

Now simplify:

5^xln((9x^4)-3x)  (36x^3-3(5^x))/(9x^4-3x)

NOTE: you can reference this website to confirm my answer: http://www.derivative-calculator.net/#

Anonymous · Answer

No, this is a product rule
with u = 5^x , v= ln((9x^4)- 3x)

---> u ' =( ln5)5^x , v ' =(36x^3 - 3)/(9x^4 - 3x)

now you can do

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Need help with this derivative?

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