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mathcalculus
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help please: Use implicit differentiation to find the equation of the tangent line to the curve at the point. (attached below)
 11 months ago
 11 months ago
mathcalculus Group Title
help please: Use implicit differentiation to find the equation of the tangent line to the curve at the point. (attached below)
 11 months ago
 11 months ago

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mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
i know i have to use implicit differentiation, then plug into derivative to find slope, plug slope and given points to pointslope formula.
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
Problem I have is step 1
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
take the derivative with respect to x. use the product rule for example, on the xy term you do this \[ \frac{d}{dx}xy = x \frac{d}{dx}y+ y \frac{d}{dx}x \\ = x \frac{dy}{dx}+ y \frac{dx}{dx} \\ = x \frac{dy}{dx}+ y\] use the same idea on \(xy^3\)
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
i got x(3y*dy/dx) +y^3
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
@phi
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
so.. 3xy*dydx +y^3
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
dy/dx**
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
you mean 3 x y^2 dy/dx for the first part d/dx of y^3 is 3 y^2 dy/dx
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
okay im lost with the second part.
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
i know that you took the derivative of xy^3= 3xy^2
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
+xy= 1?
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
*dy/dx
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
from the beginning \[ \frac{d}{dx}\left(xy^3 + xy = 4\right) \\ x \frac{d}{dx}y^3 + y^3 \frac{d}{dx}x+ x\frac{d}{dx}y+ y \frac{d}{dx}x=\frac{d}{dx}4\] that simplifies to \[ x \frac{d}{dx}y^3 + y^3+ x\frac{dy}{dx}+ y =0\] now you can do the d/dx of y^3 , right ?
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
yes.
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
use the power rule \[ \frac{d y^n}{dx} = n y^{n1} \frac{dy}{dx} \]
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
this isn't applying chain rule or is it? because i understand what youre doing here makes sense/
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
yes, it is the chain rule
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
normally you do d/dx of x^3 and you get 3x^2 dx/dx but the dx/dx is left off and the rule looks like \[ \frac{d\ x^3}{dx} = 3 x^2 \]
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
okay, let me give this a try.
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
okay I got this down: x*3y^2(dy/dx) +3y +x(dy/dx)+y=0
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
you mean y^3 not 3y , right ?
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
oh so only find the derivative of [y^3]...
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
thanks btw! :)
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
then i should just plot the points for x and y
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
wait a min. what should i do with dy/dx?
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
solve for dy/dx and then sub in for x and y to get the value of dy/dx at the point (2,1)
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
how?
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
question: is it possible to divide this: 4x/2y ????
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
how the hell can someone divide this and get 2x/y?????
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
this is so frustrating, please help me understand this.
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
@asnaseer
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
what part is confusing ? you have \[3 x y^2\frac{dy}{dx} + y^3+ x\frac{dy}{dx}+ y =0 \] plug in x=2 and y =1 and solve for dy/dx (which is the slope)
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
at the point (2,1)
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
no no, i know that. i was just looking at an example and i see that they divide 4x/2y and got 2x/y
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
it frustrated me to see this and not know how they even possibly do it.
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
are you asking how to get from \[ \frac{4x}{2y} = \frac{2x}{y} \] ? 4/2 is +2
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
yes but with diferet variables?? 0.o
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
different*
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
what is the question ?
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
oh the slope is 1/4! =]
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
yes. also, the tangent line goes through point (2,1) so you can find the intercept.
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
cool, how do you know this?
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
see http://www.khanacademy.org/math/calculus/differentialcalculus/implicit_differentiation/v/implicitdifferentiation1 and the following videos , especially http://www.khanacademy.org/math/calculus/differentialcalculus/implicit_differentiation/v/findingslopeoftangentlinewithimplicitdifferentiation
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
okie doke
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
thanks @phi you helped me so much! ^_^ so thankful
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
they asked you to find the tangent line through point (2,1) you found its slope = 1/4 you know it goes through 2,1 so in pointslope form you have y 1 = (1/4)(x2) which you can change to slopeintercept form
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
y=1/4x+3/2
 11 months ago
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