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    I'm having really trouble wrapping my head around differentiation.

    Here's one of the first questions on my sheet:

    Differentiate from first principles:
    y = (x+1)2


    Do I use the product rule?
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    Yeah probs
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    nope. the defn of a derivative of f(x) is

    f'(x)= \lim_{h \rightarrow 0} \frac{ f(x+h)-f(x)}{h} where h is small

    so you know f(x) = (x+1)^2

    so just plug it all in and stuff should cancel then take the limit
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    (Original post by chembob)
    Yeah probs
    not if you have to do it from first principles
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    (Original post by latentcorpse)
    nope. the defn of a derivative of f(x) is

    f'(x)= \lim_{h \rightarrow 0} \frac{ f(x+h)-f(x)}{h} where h is small

    so you know f(x) = (x+1)^2

    so just plug it all in and stuff should cancel then take the limit

    So I'm replacing all the xs with x+1? Is that what you mean?

    EDIT: f(x) will be replaced with (x+1)2, but how will I know what h and f(x+h) is? Is h zero?
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    (Original post by latentcorpse)
    not if you have to do it from first principles
    What's first principles?
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    Use the chain rule. Try the substitution  u = x + 1
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    (Original post by Eljamaispa)
    I'm having really trouble wrapping my head around differentiation.

    Here's one of the first questions on my sheet:

    Differentiate from first principles:
    y = (x+1)2


    Do I use the product rule?
    just use the chain rule

    let u = x + 1 ....
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    (Original post by Eljamaispa)
    So I'm replacing all the xs with x+1? Is that what you mean?

    EDIT: f(x) will be replaced with (x+1)2, but how will I know what h and f(x+h) is? Is h zero?
    f(x+h)=(x+h+1)^2 = x^2+h^2+1+2xh+2x+2h
    f(x)=(x+1)^2 = x^2+2x+1

    f(x+h)-f(x)=h^2+2xh+2h

    [f(x+h)-f(x)]/h=h+2x+2

    then take the limit and check against the chain rule
 
 
 
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