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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)
 one year ago
 one year 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)
 one year ago
 one year 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.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
Problem I have is step 1
 one year 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 \(xy^3\)
 one year ago

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

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

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

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

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
*dy/dx
 one year 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 ?
 one year ago

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

phi Group TitleBest ResponseYou've already chosen the best response.1
yes, it is the chain rule
 one year 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 \[ \frac{d\ x^3}{dx} = 3 x^2 \]
 one year ago

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

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

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

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

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

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

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

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

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
@asnaseer
 one year 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)
 one year ago

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

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

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

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

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

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

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

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

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