# derivative

1. ### Derivative of ln(-x)

Can someone please explain to me why the derivative of ln(-x) is 1/x? Thanks!
2. ### The n-th derivative of x*cos(2x)

Hey, I have to find the f^{(n)}(x) of function f(x) = x \cdot \cos(2x). I know I need to find a Leibnitz formula for derivative of product, but how? Also, I have to solve this formula explicitly, so, f^{(n)}(x) = .... Please help ;)
3. ### Calculating derivative using formal definition tricky

Can someone guide me in terms of finishing off the derivative computation that I have started below? Help is greatly appreciated!
4. ### Calculate derivative using formal definition

I'm really hoping someone can help me calculate the derivative (using the formal definition) for the following function: Here is my attempted solutions but I know it is wrong: Can someone tell me what I am doing incorrectly?
5. ### Using formal definition of a limit

Can someone help me complete the derivative computation below? I'm a bit stuck.
6. ### Creating generic formula

Hi, I'm trying to create a formula for the function $g^n(x)$ which has the following derivative pattern: $$g^1(x) = \frac{e^x(x-1) + 1}{x^2}$$ $$g^2(x) = \frac{e^x(x^2 - 2x + 2) - 2}{x^4}$$ $$g^3(x) = \frac{e^x(x^3 - 3x^2 + 6x - 6) + 6}{x^4}$$ g^4(x) = \frac{e^x(x^4 - 4x^3 +12x^2 -24x + 24)...