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anonymous
 5 years ago
how do i find the derivative of:
Y=x^3 tan^2 x
anonymous
 5 years ago
how do i find the derivative of: Y=x^3 tan^2 x

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myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0you have a function times a function so you have to use the product rule

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0so we have y'=[x^3]'(tanx)^2+x^3[(tanx)^2]'

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0(x^3)'=3x^2 using power rule

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0we have [(tanx)^2]'=2(tanx)*[secx]^2 using chain rule

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[3x^2(\tan^2x)+x^3(1/\cos^2x)\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0That's not right mmonish91

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we know the equation is uv' + u'v, so take the following:  u = x^3  u' = 3x^2  v = tan^2x  v' = 2 tanx sec^2x so: y' = uv' + u'v = (x^3)(2tanxsec^2x) + (3x^2)(tan^2x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0@myinninaya please do explain

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0mmonish dear, you started correctly, but didn't get d/dx tan^2x right. the derivative of tanx = sec^2x , but in this case the derivative of: (tanx)^ 2 = 2.(tanx)(sec^2x) ; you multiply the power first then subtract it, then you derive tanx. (power rule) ^_^ a^ u = u(a)(u') < rule :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i see...i left out the 2 for tan^2 mah bad

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0a^ u = u(a)^u1 (u') , sorry lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no problem, we all make mistakes ^_^

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i don't really work with sec so my professor said we could leave it in sin or cos format

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but you must know the derivative of tanx = sec^2x while the derivative of secx = secxtanx :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which is same as 1/cos^2x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but I see what you mean :), u left it in cos, it's alright

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you are most welcome sindy ^_^ glad you understood it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes i did understand :D ..
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