How do you differentiate $f(x) = sqrt((5x+1)^2+(2x-1))$ using the chain rule?

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Answer 1 · 2015-11-11T14:13:55

$f'(x)=frac{25x+6}{sqrt(25x^2+12x)}$

After simplifying,

$f(x)=sqrt(25x^2+12x)$ .

Let $u=25x^2+12x$ .

Then, $frac{du}{dx}=50x+12$ .

Using the chain rule,

$f'(x)=frac{d}{dx}(sqrt(25x^2+12x))$

$=frac{d}{dx}(sqrt(u))$

$=frac{d}{du}(sqrt(u))frac{du}{dx}$

$=frac{1}{2sqrt(u)}(50x+12)$

$=frac{25x+6}{sqrt(25x^2+12x)}$ .

How do you differentiate f(x) = sqrt((5x+1)^2+(2x-1))f(x) = sqrt((5x+1)^2+(2x-1)) using the chain rule?