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Find the derivative of the functionusing the chain rule. k(x)= x^2 sec(1/x)
 one year ago
 one year ago
Find the derivative of the functionusing the chain rule. k(x)= x^2 sec(1/x)
 one year ago
 one year ago

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satellite73Best ResponseYou've already chosen the best response.0
need the product rule as well
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
start with \[2x\sec(\frac{1}{x})+x^2\frac{d}{dx}\sec(\frac{1}{x})\] second part requires chain rule
 one year ago

roselinBest ResponseYou've already chosen the best response.0
the one that you have done is by using the product rule?
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
the derivative of secant is secant tangent, and the derivative of \(\frac{1}{x}\) is \(\frac{1}{x^2}\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
so the whole thing is \[2x\sec(\frac{1}{x}+x^2\sec(\frac{1}{x})\tan(\frac{1}{x})\times (\frac{1}{x^2})\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
we can clean it up a bit as \[2x\sec(\frac{1}{x})\sec(\frac{1}{x})\tan(\frac{1}{x})\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
on account of the \(x^2\) cancel
 one year ago

roselinBest ResponseYou've already chosen the best response.0
If anytime i get a problem like this, do I have to use the product rule first and then continue with the chain rule?
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
well it is not really a matter of "what goes first" you have to use the rules as you need them \(x^2\sec(\frac{1}{x})\) is a product so you need the product rule for sure also \(\sec(\frac{1}{x})\) is a composite function, so you must use the chain rule when you take the derivative
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
just like if you have a quotient, you have to use the quotient rule, but if the numerator is a product, you will need the product rule for that one and if the denominator is a composite function you will need the chain rule for it use whatever rules you need to get the derivative
 one year ago

roselinBest ResponseYou've already chosen the best response.0
i have one more question/problem.would you be willing to help me out ?
 one year ago
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