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amy0799
 one year ago
The function f and g are differentiable at x=10 and x=20 and f(g(x))=x^2. if f(10)=5, f'(10)=4, f'(20)=5, and g(10)=20, what is the value of g'(10)?
amy0799
 one year ago
The function f and g are differentiable at x=10 and x=20 and f(g(x))=x^2. if f(10)=5, f'(10)=4, f'(20)=5, and g(10)=20, what is the value of g'(10)?

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freckles
 one year ago
Best ResponseYou've already chosen the best response.3have you used chain rule to differentiate f(g(x)) yet?

amy0799
 one year ago
Best ResponseYou've already chosen the best response.1I learned how to do the chain rule

freckles
 one year ago
Best ResponseYou've already chosen the best response.3ok then what is \[\frac{d}{dx}f(g(x))=?\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3that is the product rule we don't have f*g we have f composed with g

freckles
 one year ago
Best ResponseYou've already chosen the best response.3this is why I asked you to use chain rule to differentiate f(g(x))

amy0799
 one year ago
Best ResponseYou've already chosen the best response.1I thought u use the chain rule when its something to a power

freckles
 one year ago
Best ResponseYou've already chosen the best response.3power rule is what you use when you have a constant power

freckles
 one year ago
Best ResponseYou've already chosen the best response.3chain rule is what you use when you have a function inside a function

amy0799
 one year ago
Best ResponseYou've already chosen the best response.1ooh ok. So how would I do the chain rule for this? would it be f'(g(x))*g'(x)?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[f(g(x))=x^2 \\ \text{ differentiating both sides } \\ f'(g(x)) \cdot g'(x)=2x\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3not enter in 10 for x

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[f'(g(10)) \cdot g'(10)=2(10)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3so replace g(10) with 20 \[f'(g(10)) \cdot g'(10)=2(10)\] \[f'(20) \cdot g'(10)=2(10)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3see if you can finish the rest

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[f'(20)=5 \\ \text{ so we have } \\ 5 \cdot g'(10)=2(10)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3hmmm how did you get g'(10)=25?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3you do know the operation between 5 and g'(10) is multiplication and not addition :p

freckles
 one year ago
Best ResponseYou've already chosen the best response.320/5 is 4 good worrk

amy0799
 one year ago
Best ResponseYou've already chosen the best response.1I have another question, do u mind helping me till?

amy0799
 one year ago
Best ResponseYou've already chosen the best response.1In the table below, the values of f(x), g(x), f'(x) and g'(x) are given 2 values of x. if y =[f(2x)+g(x)]^2, find y'(3)

freckles
 one year ago
Best ResponseYou've already chosen the best response.3well we know we are going to have differentiate since we want to find y'(of something)

freckles
 one year ago
Best ResponseYou've already chosen the best response.3again here you will have to use chain rule this chain rule does come with power rule because we have have a constant power we will also have to use sum rule then chain rule again

amy0799
 one year ago
Best ResponseYou've already chosen the best response.12(f(2x)+g(x))*(f'(2x)+g'(x))

freckles
 one year ago
Best ResponseYou've already chosen the best response.3ok I only have one complaint...

freckles
 one year ago
Best ResponseYou've already chosen the best response.3notice the inside function is 2x

freckles
 one year ago
Best ResponseYou've already chosen the best response.3the outside function is f( )

freckles
 one year ago
Best ResponseYou've already chosen the best response.3when you find the derivative of f(2x) w.r.t. x you should get 2*f'(2x) derivative of inside time derivative of outside

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[y(x)=[f(2x)+g(x)]^2 \\ y'(x)=2[f(2x)+g(x)] \cdot [2 f'(2x)+g'(x)]\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3now we want to find y'(3)

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\\ y'(3)=2[f(2\cdot 3)+g(3)] \cdot [2 f'(2 \cdot 3)+g'(3)]\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[f(6)=? \\ g(3)=? \\ f'(6)=? \\ g'(3)=?\] you found these values from the table ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[f(6)=3 \\ g(3)=1 \\ f'(6)=2 \\ g'(3)=5\] this is what I see for those values is that what you also see

amy0799
 one year ago
Best ResponseYou've already chosen the best response.1oh I know what I did wrong. Hold on

freckles
 one year ago
Best ResponseYou've already chosen the best response.3purrrfect (you know like a cat)

amy0799
 one year ago
Best ResponseYou've already chosen the best response.1haha thank you so much for the help!

freckles
 one year ago
Best ResponseYou've already chosen the best response.3np I hope everything makes more sense

amy0799
 one year ago
Best ResponseYou've already chosen the best response.1Yup it does thanks to your help :D

freckles
 one year ago
Best ResponseYou've already chosen the best response.3np I must go now good luck with calculus

amy0799
 one year ago
Best ResponseYou've already chosen the best response.1ok. thanks, I need all the luck I can get haha
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