Power rule and product rule problem

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  • #1
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[tex](2x+3)^3(x-4)[/tex]
How do I differentiate this?
 

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  • #2
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Use the product rule: [itex] vdu + udv [/itex]. For the first function use the power rule: [itex] x^n = nx^{n-1} \frac{du}{dx}=(3(2x+3)^2(2) [/itex]
 
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  • #3
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Ok. Thanks!
 
  • #4
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[tex]\frac{dy}{dx}=3(2x+3)^2(2) + 1[/tex]
Right?
 
  • #5
arildno
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No!
You must be more careful!
Define:
[tex]f(x)=(2x+3)^{3},g(x)=(x-4)[/tex]
Then,
[tex]y(x)=f(x)g(x),y'(x)=f'(x)g(x)+f(x)g'(x)[/tex]
You need therefore to calculate f'(x) and g'(x)
 
  • #6
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I got it! Thank you!
 

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