1. ## Derivatives

I'm stuck with these derivative problems. I've tried all the methods that I know and haven't gotten anything.

1. Find f'(x) where f(x) = $\displaystyle sqrt(4x)$. Then find f'(5)

2. Find f'(x) where f(x) = $\displaystyle 4x^2 - 3x - 27$

3. Find f'(x) where f(x) = $\displaystyle 4 + 2/x + 6/x^2$

4. Find f'(9) where f(x) = $\displaystyle 3(sqrt(x))(x^3 - 8(sqrt(x)) + 5)$

5. Find f'(x) where f(x) = 12/(t^5)

2. Originally Posted by john11235
I'm stuck with these derivative problems. I've tried all the methods that I know and haven't gotten anything.

1. Find f'(x) where f(x) = $\displaystyle sqrt(4x)$. Then find f'(5)

Mr F says: $\displaystyle {\color{red}f(x) = 2 \sqrt x = 2 x^{1/2}}$.

2. Find f'(x) where f(x) = $\displaystyle 4x^2 - 3x - 27$

3. Find f'(x) where f(x) = $\displaystyle 4 + 2/x + 6/x^2$

Mr F says: $\displaystyle {\color{red}f(x) = 4 + 2 x^{-1} + 6 x^{-2}}$.

4. Find f'(9) where f(x) = $\displaystyle 3(sqrt(x))(x^3 - 8(sqrt(x)) + 5)$

Mr F says: Expand.

5. Find f'(x) where f(x) = 12/(t^5)

Mr F says: $\displaystyle {\color{red}f(t) = 12 t^{-5}}$.
In all cases, use the first rule you would have been taught: If $\displaystyle f(x) = a x^n$ then $\displaystyle f'(x) = n a x^{n-1}$.

Differentiate term-by-term as required. Then substitute the given value of x.