# Thread: Quotient Rule, differentiate the function

1. ## Quotient Rule, differentiate the function

Hi Everyone,

This question is about the quotient rule, I'm stuck for how to develop it!

Here is the question and my answer:

Write down the derivative of each of the functions
f(t)= t^4 +5 and g(t) = ln(3t) (t>0).

Derivative:
f ‘(t) = 4t3+5
g ‘(t) = 1/3t

Hence, by using the Quotient Rule, differentiate the function
k(t)= t4+5 (t > 1/3).
ln(3t)

Quotient rule:
k ‘(t) = g(x) f ‘(x) – f(x) g ‘(x)
(g(x))2

k ’(t) = (In(3t)) (4t3) – (t4+5) (1/3t)
(In(3t))2e

I don't think I'm doing it right. How to differentiate the function with the quotient rule? that is as far I did it

Can someone help me

2. Hello Valerie

Flying squirrel helped me with quotient rule, hopefully now I can help you!

I think $g'(t) = 1/t$ as $U=3t$ gives $du/dt=3$ and $dg/du=1/u$. using chain rule $3/3t$ gives $1/t$.

Your initial $f't$ should be $4t^3$ but it was ok when inserted in formula.

hopefully this is right, i'm sure someone will correct if not, they are very good on here!