Find Derivative Using Delta Process

**magentarita** · February 15th 2009, 12:44 PM

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?

**Moo** · February 15th 2009, 12:53 PM

Hello,

Originally Posted by magentarita

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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