1. ## Derivative of 3x^2+6x+5/Sqrt(x)

How do I solve this?

2. ## Re: Derivative of 3x^2+6x+5/Sqrt(x)

Originally Posted by rhcprule3
How do I solve this?
First of all is this
$\displaystyle 3x^2 + 6x + \frac{5}{\sqrt{x}}$

or
$\displaystyle \frac{3x^2 + 6x + 5}{\sqrt{x}}$

-Dan

3. ## Re: Derivative of 3x^2+6x+5/Sqrt(x)

in any case just use the formula d(x^n)/dx = nx^(n-1) also remember derivative of sum or difference of functions is sum or difference of derivatives. ie., ( u+/- v)' = u' +/ - v'

4. ## Re: Derivative of 3x^2+6x+5/Sqrt(x)

So for the deivative I would get 6x+6-5/2(x^(-7/2))?

5. ## Re: Derivative of 3x^2+6x+5/Sqrt(x)

the question is (3x^2+6x+5)/(Sqrt(x))

6. ## Re: Derivative of 3x^2+6x+5/Sqrt(x)

Your answer is not right. You can approach this in either of two ways:

1. Divide the denominator into the numerator to get $\displaystyle f(x) = 3 x^{3/2} + 6x^{1/2} + 5x^{-1/2}$ Now get the derivative using the same techniques as in your other posts, where the derivative of $\displaystyle x^n$ is $\displaystyle n x^{n-1}$.

2. Use the formula for derivates of one function divided by another: the derivative of $\displaystyle \frac {f(x)}{g(x)}$ is: $\displaystyle \frac {f'(x) g(x) - f(x)g'(x)}{(g(x))^2}$. Here $\displaystyle f(x) = 3x^2+6x+5$ and $\displaystyle g(x) = x^{1/2}$.

Both approaches give the same answer.

7. ## Re: Derivative of 3x^2+6x+5/Sqrt(x)

thanks. man i cant believe i didnt even think of that, brainfart i guess...