Can this simplify further - if so, what's the next step?

[RapidAssistant]

I have been trying to differentiate this particular function - (which I know how to do) :

So therefore I get the result using the quotient rule:



I know that the correct answer is:

But I don't know how to get there

 

[blamocur]

Start by bringing both fractions to a common denominator ?

 

[Otis]

Hi RapidAssistant. After you finish simplifying your result from the Quotient Rule, try differentiating with the Product Rule to compare methods. You might find one more rapid.

\(\displaystyle (4x + 3)^{4} (x + 1)^{-3}\)

?

 

[Steven G]

You never should have broken up the fraction into two fraction. You should have factored that numerator and see what happens with that.

 

[Deleted member 4993]

I have been trying to differentiate this particular function - (which I know how to do) :View attachment 29504

So therefore I get the result using the quotient rule:

View attachment 29506

I know that the correct answer is: View attachment 29507

But I don't know how to get there

after applying quotient rule, you get:

\(\displaystyle \frac{16(x+1)^3(4x+3)^3 - 3(x+1)^2(4x+3)^4}{(x+1)^6}\)

Now simplify the numerator by factoring out the common factors.