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mlddmlnog

  • 2 years ago

let f and g be differentiable functions such that f(1)=2 f'(1)=3 f'(2)=-4 g(1)=2 g'(1)=-3 g'(2)=5 if h(x)=f(g(x)), then h'(1)=?

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  1. mlddmlnog
    • 2 years ago
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    the answer is 12.

  2. mlddmlnog
    • 2 years ago
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    @zepdrix

  3. zepdrix
    • 2 years ago
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    So you have to kind of remember the DEFINITION of the chain rule for this one.

  4. zepdrix
    • 2 years ago
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    \[\large h(x)=f(g(x))\]The chain rule will produce this.\[\large h'(x)=f'(g(x))\cdot g'(x)\]

  5. mlddmlnog
    • 2 years ago
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    oh.. wait. i'll try to do it myself now. thank you for giving me a start! :)

  6. mlddmlnog
    • 2 years ago
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    yay i got it :)

  7. zepdrix
    • 2 years ago
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    yay

  8. mlddmlnog
    • 2 years ago
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    here i the next one that's kind of similar to this. but i don't get. If \[f(x)=x ^{3}+3x ^{2}+4x+5\] and g(x)=5, then g(f(x))=?

  9. zepdrix
    • 2 years ago
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    Hmmmmm....

  10. mlddmlnog
    • 2 years ago
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    The answer is 5.

  11. zepdrix
    • 2 years ago
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    So here is how a composition of functions works. Everywhere you see an x, you replace it with f(x). Example:\[\large \color{orangered}{f(x)=2x}\]\[\large g(\color{cornflowerblue}{x})=\color{cornflowerblue}{x}+3\] \[\large g(\color{orangered}{f(x)})=\color{orangered}{f(x)}+3\]

  12. zepdrix
    • 2 years ago
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    In the problem we've been given, the function \(g(x)\) is CONSTANT. There are no x's! So when we plug f(x) into it, it should give us the same answer, because g(x) is always 5. Always constant. You could do the composition thing I explained earlier and it might make sense. If you try to plug in f(x) for any x's in g, you'll see that you have nowhere to actually plug it in.

  13. zepdrix
    • 2 years ago
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    Is your teacher any good? Because so far I'm really really disliking these problems. None of them are straight forward. It just feels like he gave you a list of puzzles to work on.

  14. mlddmlnog
    • 2 years ago
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    haha yes. she loves these types of questions. -_____- all of her questions are like this. making our brains explode. it literally takes me like 8 hours to do hw. it's insane.

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