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amyna
 one year ago
y=3(sec^2x  tan^2(x)) + 4x^3
I do not know how to solve this! Please help with the calc problem!! Thank you!
amyna
 one year ago
y=3(sec^2x  tan^2(x)) + 4x^3 I do not know how to solve this! Please help with the calc problem!! Thank you!

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freckles
 one year ago
Best ResponseYou've already chosen the best response.2recall Pythagorean identities \[\sin^2(x)+\cos^2(x)=1 \\ \text{ divide both sides by } \cos^2(x) \\ \tan^2(x)+1=\sec^2(x) \\\] anyways I don't know what it is meant by solve

freckles
 one year ago
Best ResponseYou've already chosen the best response.2could you say what solve means here @amyna if you are here

freckles
 one year ago
Best ResponseYou've already chosen the best response.2you say this is a cal problem do you really mean differentiate are you trying to find the inverse like what are you doing exactly

amyna
 one year ago
Best ResponseYou've already chosen the best response.0yup sorry! differentiate it, thanks!

freckles
 one year ago
Best ResponseYou've already chosen the best response.2so you need help to differentiate 3+4x^3 just use constant rule and constant multiple rule and power rule?

freckles
 one year ago
Best ResponseYou've already chosen the best response.23 is a constant the derivative of a constant is 0

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{d}{dx} cx^n \\ c \frac{d}{dx} x^n \text{ by constant multiple rule } \\ c n x^{n1} \text{ by power rule }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{d}{dx}(3)=? \\ \frac{d}{dx}4x^3=?\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2where did all the sec and tan stuff come from

freckles
 one year ago
Best ResponseYou've already chosen the best response.2did you use the Pythagorean identity earlier ? you should y=3+4x^3

freckles
 one year ago
Best ResponseYou've already chosen the best response.2and we are wanting to find y' now

freckles
 one year ago
Best ResponseYou've already chosen the best response.2though if you really want to differentiate sec^2(x)tan^2(x) which is a constant so the derivative should be 0 but pretending you don't know you should wind up with this: \[\frac{d}{dx} \sec^2(x)=2 \sec(x) \cdot \sec(x)\tan(x) =2\sec^2(x)\tan(x) \\ \frac{d}{dx} \tan^2(x)=2 \tan(x) \sec^2(x) =2 \sec^2(x)\tan(x) \\ \text{ but as you notice } \\ \frac{d}{dx} \sec^2(x)\frac{d}{dx} \tan^2(x)=0 \\ \frac{d}{dx}(\sec^2(x)\tan^2(x))=0\] this is because \[\sec^2(x)\tan^2(x) \text{ is a constant } \\ \text{ this is because } \sec^2(x)\tan^2(x)=1 \text{ for all } x \text{ on it's domain }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2but as I said all of that work is unnecessary

freckles
 one year ago
Best ResponseYou've already chosen the best response.2your y really just say y=3+4x^3

amyna
 one year ago
Best ResponseYou've already chosen the best response.0so what is the final answer?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2do you know how to differentiate 3 and 4x^3?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2ok great then why are you asking me what y' is when you know \[y=3+4x^3 \\ y'=0+12x^2 \\ y'=12x^2 \]

amyna
 one year ago
Best ResponseYou've already chosen the best response.0oh okay! i was looking at it wrong! now i get it! thank you so much!
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