# Thread: Derivatives with x and h variables

1. ## Derivatives with x and h variables

Limit of h goes to 0 $\displaystyle [2(x+h)^2+5(x+h)^4]-[2x^2+5x^4]/h=?$
(Hint: This is the definition of the derivative.)

Obviously the hint is giving me a big clue, but I don't understand the concept. My limits are kinda rusty, and I'm not sure what to do. Help Please.

2. Originally Posted by DarkestEvil
Limit of h goes to 0 $\displaystyle [2(x+h)^2+5(x+h)^4]-[2x^2+5x^4]/h=?$
(Hint: This is the definition of the derivative.)

Obviously the hint is giving me a big clue, but I don't understand the concept. My limits are kinda rusty, and I'm not sure what to do. Help Please.
you don't need to "work out" the limit ... all you have to do is remember that

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

... you have $\displaystyle f(x)$.

3. Originally Posted by DarkestEvil
Limit of h goes to 0 $\displaystyle [2(x+h)^2+5(x+h)^4]-[2x^2+5x^4]/h=?$
(Hint: This is the definition of the derivative.)

Obviously the hint is giving me a big clue, but I don't understand the concept. My limits are kinda rusty, and I'm not sure what to do. Help Please.
Just expand and do the algebra.
$\displaystyle (x+h)^2=x^2+2xh+h^2$

$\displaystyle (x+h)^4=x^4+4x^3h+6x^2h^2+4xh^3+h^4$

4. Originally Posted by DarkestEvil
Limit of h goes to 0 $\displaystyle [2(x+h)^2+5(x+h)^4]-[2x^2+5x^4]/h=?$
(Hint: This is the definition of the derivative.)

Obviously the hint is giving me a big clue, but I don't understand the concept. My limits are kinda rusty, and I'm not sure what to do. Help Please.
$\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$

So in this example, $\displaystyle f(x)=2x^2+5x^4$ and therefore, using the power rule, the limit equals $\displaystyle f'(x)=4x+20x^3$.