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

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mathcalculusBest 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.
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
Problem I have is step 1
 8 months ago

phiBest 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 \(xy^3\)
 8 months ago

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

mathcalculusBest ResponseYou've already chosen the best response.1
so.. 3xy*dydx +y^3
 8 months ago

phiBest 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
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
okay im lost with the second part.
 8 months ago

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

phiBest 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 ?
 8 months ago

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

mathcalculusBest 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/
 8 months ago

phiBest 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 \[ \frac{d\ x^3}{dx} = 3 x^2 \]
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
okay, let me give this a try.
 8 months ago

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

phiBest ResponseYou've already chosen the best response.1
you mean y^3 not 3y , right ?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
oh so only find the derivative of [y^3]...
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
then i should just plot the points for x and y
 8 months ago

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

phiBest 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)
 8 months ago

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

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

mathcalculusBest ResponseYou've already chosen the best response.1
this is so frustrating, please help me understand this.
 8 months ago

phiBest 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)
 8 months ago

mathcalculusBest 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
 8 months ago

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

phiBest 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
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
yes but with diferet variables?? 0.o
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
oh the slope is 1/4! =]
 8 months ago

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

mathcalculusBest ResponseYou've already chosen the best response.1
cool, how do you know this?
 8 months ago

phiBest 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
 8 months ago

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

phiBest 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
 8 months ago
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