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mathcalculusBest ResponseYou've already chosen the best response.0
\[\sqrt{86*X^2}\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
the derivative of \(\sqrt{f(x)}\) is \[\frac{f'(x)}{2\sqrt{f(x)}}\]
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
can we do this step by step please.
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
the steps are what i wrote above take the derivative of \(86x^2\) and by the power rule, you get \(12x\) that goes in the numerator in the denominator you put \(2\sqrt{86x^2}\)
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
oh... why do we put that as the denominator?
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
all that is left to do is cancel a 2 top and bottom
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
the derivative of \(\sqrt{x}\) is \(\frac{1}{2\sqrt{x}}\) therefore by the chain rule the derivative of \(\frac{1}{f}\) is \(\frac{f'}{2\sqrt{f}}\) where \(f\) is any function
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
for example, the derivative of \(\sqrt{\sin(x)}\) is \[\frac{\cos(x)}{2\sqrt{\sin(x)}}\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
the derivative of \[\sqrt{3x^2+2x}\] is \[\frac{6x+2}{2\sqrt{3x^2+2x}}\]
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
after i have 12x/ 2radical 86x^2.. how can i find the critical points?
 one year ago
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