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Math Help - Find Derivative Using Delta Process

  1. #1
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    Find Derivative Using Delta Process

    Find the derivative using the delta process.

    f(x) = kx + c

    MY WORK:

    f'(x) = lim as h--->0 for kx + c

    f'(x) = lim as --->0 f(x + h) - f(x)/h

    f'(x) = lim as --->0 k(kx + c + h) - kx + c

    f'(x) = lim as --->0 kx + kc + kh - kx + c

    This is where I get stuck.

    The answer is simply k but how do I find the answer using the delta process?


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  2. #2
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    Hello,
    Quote Originally Posted by magentarita View Post
    Find the derivative using the delta process.

    f(x) = kx + c

    MY WORK:

    f'(x) = lim as h--->0 for kx + c

    f'(x) = lim as h--->0 f(x + h) - f(x)/h

    f'(x) = lim as h --->0 k(kx + c + h) - kx + c

    f'(x) = lim as --->0 kx + kc + kh - kx + c

    This is where I get stuck.

    The answer is simply k but how do I find the answer using the delta process?


    I don't exactly know how you messed up... there are some problems in red...


    f'(x)=\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}

    What is f(x+h) ?
    We know that f({\color{blue}x})=k{\color{blue}x}+c
    f({\color{red}x+h})=k({\color{red}x+h})+c=kx+kh+c

    So f'(x)=\lim_{h \to 0} \frac{(kx+kh+c)-(kx+c)}{h}

    Beware of the negative sign ! -(kx+c)=-kx-c \neq -kx+c

    So f'(x)=\lim_{h \to 0} \frac{kx+kh+c-kx-c}{h}=\lim_{h \to 0} \frac{(kx-kx)+kh+(c-c)}{h}=\lim_{h \to 0} \frac{kh}{h}=k

    Is it better this way ?
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