Question

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

f(x) = square root 5x+x^2 << all under root

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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.

Answer 6

i got 2x(5x+x^2)

... is that correct? i had a bit of trouble after plugging the equation in

Answer 7

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

Answer 8

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