# Thread: Use the definition of Derivative to find f(x)

1. ## Use the definition of Derivative to find f(x)

1. f(x) = 4
(√5 - x)

Note: 5 - x is all squared.

2. f(x) = 2x
x - 2

3. f(x) =
√x + 2
3

2. Originally Posted by valeriegriff
1. f(x) = 4
(√5 - x)

Note: 5 - x is all squared.
Is it all squared or all in the square root? A clearer way of writing that would be 4/√(5- x). Use parentheses!

That is equal to $\displaystyle 4(5- x)^{-1/2}$. Use the "power rule" (derivative of $\displaystyle x^n$ is $\displaystyle n x^{n-1}$ and the chain rule.

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2. f(x) = 2x
x - 2
f(x)= 2x/(x- 2). Use the quotient rule!

3. f(x) = √x + 2
3
$\displaystyle (1/3)(x+2)^{1/2}$

Again, "power rule" and "chain rule".

3. i understand the concept of rules. but the problem i am having with these questions is that i was asked to find the derivative using the definition. i know the definition is
f(x) = f( x + h) - f(x) Żall over- h

but when i place the equations into the definition i cannot get the same answer as the rules. there is something i am doing wrong and i dont know what..