Calculate the derivative of the function.
( Using Chain Rule)

f(x) = square root 5x+x^2

Question

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

callisto · Answer

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

callisto · Answer

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.

anonymous · Answer

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

anonymous · Answer

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

callisto · Answer

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