## anonymous 4 years ago Calculate the derivative of the function. ( Using Chain Rule) f(x) = square root 5x+x^2 << all under root

1. anonymous

$\frac{d}{dx}[\sqrt{f(x)]}=\frac{f'(x)}{2\sqrt{f(x)}}$

2. anonymous

use $$f(x)=5x+x^2,f'(x)=5+2x$$ plug and be done

3. anonymous

just plug 5+2x into which part of the equation?

4. Callisto

Let u = 5x+x^2 $f'(x) = \frac{d}{du}\sqrt u \times \frac{d}{dx}(5x+x^2)=...?$

5. Callisto

First, find d/du (sqrt u) Then find d/dx (5x + x^2) Next, multiply the two results Finally, replace u by 5x+x^2.

6. anonymous

i got 2x(5x+x^2) ... is that correct? i had a bit of trouble after plugging the equation in

7. anonymous

$\sqrt{5+x^2}\times(5x+x)^2$

8. Callisto

$\frac{d}{du} \sqrt u = \frac{1}{2 \sqrt u}$ $\frac{d}{dx} (5x+x^2)= 5 + 2x$ Multiply the two results, and sub y = 5x+x^2 back to the answer you get..