anonymous
  • anonymous
Calculate the derivative of the function. ( Using Chain Rule) f(x) = square root 5x+x^2 << all under root
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\frac{d}{dx}[\sqrt{f(x)]}=\frac{f'(x)}{2\sqrt{f(x)}}\]
anonymous
  • anonymous
use \(f(x)=5x+x^2,f'(x)=5+2x\) plug and be done
anonymous
  • anonymous
just plug 5+2x into which part of the equation?

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Callisto
  • Callisto
Let u = 5x+x^2 \[f'(x) = \frac{d}{du}\sqrt u \times \frac{d}{dx}(5x+x^2)=...?\]
Callisto
  • 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.
anonymous
  • anonymous
i got 2x(5x+x^2) ... is that correct? i had a bit of trouble after plugging the equation in
anonymous
  • anonymous
\[\sqrt{5+x^2}\times(5x+x)^2\]
Callisto
  • 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..

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