Question

what is the first and second derivative of (2x-3)(x+4)^-1

Answer 1

\[f' = \frac{-2x+3}{(x+4)^{2}}+\frac{2}{x+4} = \frac{11}{(x+4)^{2}}\]

Answer 2

\[f'' = \frac{22}{(x+4)^{3}}\]

Answer 3

\[f'' = -\frac{22}{(x+4)^{3}}\]

You missed the minus.

Answer 4

It's very unreadable, so I'm just going to say that you're wrong and give you proof:
http://www.wolframalpha.com/input/?i=derive+%282x-3%29%28x%2B4%29^-1

Answer 5

how do u get 11?

Answer 6

Are you familiar with the quotient rule? If we apply that we get for nominator: 2(x+4)-1(2x-3)=11

Answer 7

by multiplying the right side by \[\frac{x+4}{x+4}\] and simplifying after using the product rule, or as thomas said, by the quotient rule.

Answer 8

what about the derivative of \[\sqrt{x}\left( 2x+3 \right)^{2}\]

Answer 9

product rule \[uv' + vu'\]