differentiate the function f(x)= x+1/ 5-2x and simplify

[yanarains]

Differentiate the given function and simplify your answer

f(x)= x+1/ 5-2x

f(x)= (5-2x)x 1 - (x+1)x 2/ (5-2x)^2

= 5-2x -2x+1 / (5-2x)^2
= 4x-6 / (5-2)^2

Am I doing this problem right? I thought I wanted to cancel out the x's using the quotient rule but in this case they don't cancel out.

 

[stapel]

Differentiate the given function and simplify your answer

f(x)= x+1/ 5-2x...

I will guess that you mean the following:

. . . . .f(x) = (x + 1)/(5 - 2x)

...since the function, as posted ("x + (1/5) - 2x"), doesn't make much sense.

f(x)= (5-2x)x 1 - (x+1)x 2/ (5-2x)^2 ....

I will guess that you mean that "f(x)" actually to be an "f'(x)", since the second f(x) is not equivalent to the first f(x). Also, I will guess that you are using "x" to be both the variable and the "multiplication" symbol "*" or "×". Also, I will guess that lots of grouping symbols were omitted. So I think you actually mean the following:

. . .f'(x) = [(1)(5 - 2x) - (x + 1)(-2)] / [5 - 2x]^2

. . . . . . .= [5 - 2x - (-2x - 2)] / [5 - 2x]^2

. . . . . . .= [5 - 2x + 2x + 2] / [5 - 2x]^2

...and so forth.

= 5-2x -2x+1 / (5-2x)^2

If my guesses above are correct, then it appears that you lost a "minus" sign somewhere.

= 4x-6 / (5-2)^2

What happened to the "x" in the denominator?

I thought I wanted to cancel out the x's using the quotient rule but in this case they don't cancel out.

I'm not sure why you think the Quotient Rule "cancels out x's"...? All the Quotient Rule does is give you a rule for finding the derivative of a quotient. There is no "cancellation" that I'm aware of, and you aren't asked to "cancel", only differentiate.

Please reply with correction or confirmation. Thank you!

Eliz.

 

[yanarains]

Yeah that is exactly what I was implying!!!! I actually figured it out too. I never carried over the - sign. Sorry I'm new to this math online stuff and haven't gotten used to grouping the problem correctly for everyone to see exactly what I am talking about.

Thanks for your help

 

[stapel]

I'm new to this math online stuff and haven't gotten used to grouping the problem correctly for everyone to see exactly what I am talking about.

No worries! :wink:

Figuring out how to write math "sideways" (like typed-out words) instead of "vertically" (like you would hand-write it) is often very awkward. The following should be somewhat helpful:

. . . . .Karl's Notes for Email (leading article on the topic)

. . . . .Formatting Math as Text

In general, the prevailing rule is that "Parentheses are our friends!" :lol:

Eliz.