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

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

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1Problem I have is step 1

phi
 one year ago
Best ResponseYou've already chosen the best response.1take 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 \(xy^3\)

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

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

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

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

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

phi
 one year ago
Best ResponseYou've already chosen the best response.1from 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 ?

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

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

phi
 one year ago
Best ResponseYou've already chosen the best response.1normally 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 \[ \frac{d\ x^3}{dx} = 3 x^2 \]

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

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

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

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

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

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

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

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

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

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

phi
 one year ago
Best ResponseYou've already chosen the best response.1what 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)

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

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1it frustrated me to see this and not know how they even possibly do it.

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

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

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

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

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

phi
 one year ago
Best ResponseYou've already chosen the best response.1see 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

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

phi
 one year ago
Best ResponseYou've already chosen the best response.1they 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
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