Use the definition of Derivative to find f`(x)

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October 2nd 2009, 01:29 PM
valeriegriff

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
October 2nd 2009, 02:08 PM
HallsofIvy

Quote:

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

Quote:

[SIZE=5]
2. f(x) = 2x
x - 2

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

Quote:

3. f(x) = √x + 2
3

$(1/3)(x+2)^{1/2}$

Again, "power rule" and "chain rule".
October 8th 2009, 04:04 PM
valeriegriff

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) ¯all 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..

please help..
October 8th 2009, 04:09 PM
mr fantastic

Quote:

Originally Posted by valeriegriff

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) ¯all 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..

please help..

Show all your work and then someone can point out what you're doing wrong.