I completely forgot how to find derivatives, can someone give me an example of a simple equation and how to find its derivative? The only thing I remember is that the formula is$$f'(x)=\frac{f(x+h)-f(x)}{h}$$ Thanks for the help.
Asked
Active
Viewed 142 times
5
-
$f'(x)$ is the limit of the fraction as $h$ tends to $0$. – Bernard Sep 15 '16 at 23:40
-
4http://www.dummies.com/education/math/calculus/the-basic-differentiation-rules/ – Spencer Sep 15 '16 at 23:41
-
@Spencer Thanks, that helped to jog my memory – Randomizer Sep 15 '16 at 23:47
1 Answers
6
An easy example would be the derivative of $x^2+2x-1$.
The formula for finding derivatives, as you said, $$f'(x)=\lim_{h\to0}\frac{f(x_0+h)-f(x_0)}{h}$$ After substituting $x^2+2x+1$ into the formula, you get $$f'(x)=\frac{x^2+2hx+h^2-2h+2x+2h-1-x^2-2x+1}h=$$ $$f'(x)=\frac{h^2+2hx+2h}h=$$ $$h+2x+2$$ You find the equation as $h\rightarrow0$, so you substitute $0$ for $h$ and you get the answer: $$2x+2$$
suomynonA
- 6,895
-
1In both the question and this answer there's a limit missing in the first equation. The derivative isn't the difference quotient. – Ethan Bolker Sep 15 '16 at 23:39
-
1@EthanBolker Oops, I recognized the formula OP wrote so I got a bit confused. Thanks for pointing that out! – suomynonA Sep 15 '16 at 23:41
-
1