1. ## differentiation question

Hello, I am having trouble understanding how to differentiate this polynominal.
Can someone please outline the steps. I want to use the Newton and Leibniz method rather than the first principles formuls.
Thanks kindly for any help.

4√x +4/x

2. $\displaystyle \displaystyle 4\sqrt{x} + \frac{4}{x} = 4x^{\frac{1}{2}} + 4x^{-1}$.

Now differentiate each term.

3. thanks, I can get the second term, but still cannot get the correct answer for the first term (4√x).
What is the answer for that first term ? Then I will be able to understand.

Thanks

(for the first term, I am getting 2/x^1/2, but I dont think that is correct.)

4. $\displaystyle \displaystyle \frac{d}{dx}\left(4x^{\frac{1}{2}}\right) = \frac{1}{2}\cdot 4x^{\frac{1}{2} - 1}$

$\displaystyle \displaystyle = 2x^{-\frac{1}{2}}$

$\displaystyle \displaystyle = \frac{2}{x^{\frac{1}{2}}}$

$\displaystyle \displaystyle = \frac{2}{\sqrt{x}}$.

So you are correct.

5. The first term (4√x)
f(x) = (1\2√x).4 = 2\√x

The seconed term
f(4\x ) = (-1.4 )\ x^2 = -4\x^2