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

Question

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

$$f'' = -\frac{22}{(x+4)^{3}}$$

You missed the minus.

anonymous · Answer

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

anonymous · Answer

how do u get 11?

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

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

anonymous · Answer

product rule $$uv' + vu'$$