Understanding Derivatives: Finding the Derivative of y=2x^2-5

[chrisdapos]

Hello, today my teacher presented us with the concept of derivatives. I was okay in class, but when I got home, I was completely lost. Using the definition (f(x+h) - f(x))/h, we have to fine the derivative of y=2x^2 - 5. I know the answer is 4x from the back of the book, but I can't understand how to get it. Am I factoring something wrong? I get to a point of simplification that everything just cancels out. Your help is greatly appriciated!

 

[assyrian_77]

The definition you want to use is this:

$$\lim_{h\rightarrow 0}\frac{f(x+h) - f(x)}{h}$$

Now, set $f(x)=2x^2-5$ and insert this in the expression, simplify and take the limit.

 

[topsquark]

Quick check: When you expand the numerator, f(x+h)-f(x), you should get an expression that cancels the h in the denominator.

-Dan

 

[chrisdapos]

my problem is when i simplify, i get 0 over 0...i don't know why...i can't get the h to go away in the denominator

 

[topsquark]

my problem is when i simplify, i get 0 over 0...i don't know why...i can't get the h to go away in the denominator

$$f(x+h)=2(x+h)^2-5=2x^2+4xh+2h^2-5$$
and
$$f(x)=2x^2-5$$
So when you subtract the two you get...

-Dan

 

[assyrian_77]

Then you must be doing something wrong. Remember this: If $f(x)=2x^2-5$, what is then $f(x+h)$? Check your calculations again.

 

[chrisdapos]

Thank you so much guys! Wow i feel dumb...turns out i was just plugging the functions in wrong. Thank you so much!

 

[topsquark]

Thank you so much guys! Wow i feel dumb...turns out i was just plugging the functions in wrong. Thank you so much!

Hey, as I always tell my students: it's only a dumb question when you DON'T ask it!

-Dan