Derivatives

**john11235** · October 12th 2008, 11:05 AM

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) = $sqrt(4x)$ . Then find f'(5)

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

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

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

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

**mr fantastic** · October 12th 2008, 12:14 PM

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) = $sqrt(4x)$ . Then find f'(5)

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

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

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

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

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

Mr F says: Expand.

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

Mr F says: ${\color{red}f(t) = 12 t^{-5}}$ .

In all cases, use the first rule you would have been taught: If $f(x) = a x^n$ then $f'(x) = n a x^{n-1}$ .

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

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