Differentiation by the chain rule

  • Thread starter jtt
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  • #1
jtt
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Homework Statement


Find the derivative of the following:


Homework Equations


Y= x^3(5x-1)^4


The Attempt at a Solution


4(3x^2(5x-1)^3)(4(3x^2(3(5x-1)^2)(2(5x-1)(5)
 

Answers and Replies

  • #2
Dick
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That doesn't look like the chain rule to me. Apply the product rule first.
 
  • #3
jtt
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i tried bringing down the 4Th exponent and then subtract it by one to get three, then leaving the inside alone ( 5x-1) at the same time taking the derivative of 3x^2. after that i got confused and got a wrong answer.
 
  • #4
jambaugh
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[itex] y = f(x)g(x)[/itex] where [itex]f(x)= x^3[/itex] and [itex]g(x)=(5x-1)^4[/itex]
So you'll first need to apply the product rule... as you do you'll need the derivative of g.

[itex] g(x) = P\circ L (x) = P( L(x))[/itex] where [itex] P(x) = x^4[/itex] and [itex] L(x)=5x - 1[/itex]. As a composition you need to apply the chain rule. (P for power, L for linear).

If you'd rather use the Leibniz notation form of the chain rule: [itex]\frac{du}{dx} = \frac{du}{dv} \frac{dv}{dx}[/itex] then let u=g(x) = P(v) with v = L(x).
 
  • #5
Dick
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Your function is f*g where f=x^3 and g=(5x-1)^4, right? The product rule says the derivative of f*g is f'*g+f*g', also right? Now you just need to find f' and g'. Finding the derivative of g' is where you need the chain rule.
 

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