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)}#.