# Calculating value of f'(x)

1. Nov 21, 2009

### Macroer

1. The problem statement, all variables and given/known data
[f(x)]^5 + f(x)/(7x^2)=4
when f(2)=3, calculate f'(2)

2. Relevant equations

3. The attempt at a solution
Attachment has solution

I am stuck. I don't know if I am right upto there.

#### Attached Files:

• ###### latex.png
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2. Nov 21, 2009

### Dick

I can't see your attachment. But just take the derivative of both sides of the equation and solve for f'(x).

3. Nov 22, 2009

### HallsofIvy

Staff Emeritus
Here is what is in the attachment:
That has a sign wrong- either drop the parentheses or write
$$f'(x)= 56x- (14x\left[f(x)\right]^5+ 35x^2\left[f(x)\right]^4 f'(x))$$

and you now have the sign right!

Now, just solve for f'(2): add 11340f'(2) to both sides and divide by 11341.