Could someone please HELP with this question?!? Totally confused?

Question

Let f(x) = (x^2 + 3)^2(x^3 – 2)^3/(4x – 1)^5. Determine f ‘ (x). Leave the derivative in un-simplified form.

Answer 1

Let: f(x)= A(x) B(x) C(x)
then, f '(x)= AB C '(x) + C (AB)'
where C (AB)' = CA B' + CB A',
where A=(x^2 + 3)^2
B=(x^3 - 2)^3
C=(4x - 1)^(-5)

Answer 2

Thank goodness they'll accept the un-simplified form!

If you're confused because it seems like the problem will take a lot of calculation and have a very long answer... then you're not confused, you actually have good insight. This problem requires the use of many differentiation rules.

At the heart of the problem is the quotient rule. You have a horrendous expression on the top and a nicer one on the bottom. Use the quotient rule to set up the structure of your answer. Now you have reduced the problem to finding the derivatives of the top and bottom individually and plugging them into the quotient rule formula.

The derivative of the top will involve multiple applications of the chain rule, and at least one of the product rule. The derivative of the bottom comes out quickly with the chain rule.

Now the problem has been reduced to using rules that you know. Over and over and over. It's a pain, but just take it one step at a time.

Answer 3

Use quotient rule and product rule. This will look messy.
f'(x) = [(4x-1)^5[(x^2+3)^2(3(x^3-2)^2*3x^2+2(x^2+3)(2x)(x^3-2)^3-(x^2+3)^2(x^3-2)^3(5(4x-1)^4)(4)]/(4x-1)^10.

I can't get the entire solution to be printed. Must be some flaw in ANSWERS.

Answer 4

Let f(x) = (x^2 + 3)^2(x^3 – 2)^3/(4x – 1)^5.

for explaining i write
Let f(x) = u(x)v(x)w(x)
f' = u'vw + uv'w + uvw'

so with for example
u = (x^2 + 3)^2
u'=2(x^2 + 3)*2*x

Answer 5

f(x) = (x^2 + 3)^2(x^3 – 2)^3/(4x – 1)^5

y'=[2( (x^2 + 3)*2x*(x^3 – 2)^3
+ 3(x^3 – 2)^2 *3x^2*(x^2 + 3)^2]

*[(4x – 1)^5]- {[5*4*(4x – 1)^4* (x^2 + 3)^2(x^3 – 2)^3}

over

(4x – 1)^10

Answer 6

Really simple.....
Roll with me.
Fx means visual effect
SO visual effect = let x be 500
so your answer is 50002 = x3yr which means 23
so simplified your answer is 75million.

Answer 7

i had spend 15 min in solving this but its tooo big
we have to remove f(x+h) its too difficult