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Question 3
Тips
smartsolve

7.7pts
If 
x^(3)+3xy+2y^(3)=17, then in terms of 
x and 
y,(dy)/(dx)=

-((x^(2)+y)/(x+2y^(2)))

-((x^(2)+y)/(x+2y))

-((x^(2)+y)/(2y^(2)))

-((x^(2)+y)/(x+y^(2)))

Question 33\newlineТips\newlinesmartsolve\newline7.7pts 7.7 \mathrm{pts} \newlineIf x3+3xy+2y3=17 x^{3}+3 x y+2 y^{3}=17 , then in terms of x x and y,dydx= y, \frac{d y}{d x}= \newline(x2+yx+2y2) -\left(\frac{x^{2}+y}{x+2 y^{2}}\right) \newline(x2+yx+2y) -\left(\frac{x^{2}+y}{x+2 y}\right) \newline(x2+y2y2) -\left(\frac{x^{2}+y}{2 y^{2}}\right) \newline(x2+yx+y2) -\left(\frac{x^{2}+y}{x+y^{2}}\right)

Full solution

Q. Question 33\newlineТips\newlinesmartsolve\newline7.7pts 7.7 \mathrm{pts} \newlineIf x3+3xy+2y3=17 x^{3}+3 x y+2 y^{3}=17 , then in terms of x x and y,dydx= y, \frac{d y}{d x}= \newline(x2+yx+2y2) -\left(\frac{x^{2}+y}{x+2 y^{2}}\right) \newline(x2+yx+2y) -\left(\frac{x^{2}+y}{x+2 y}\right) \newline(x2+y2y2) -\left(\frac{x^{2}+y}{2 y^{2}}\right) \newline(x2+yx+y2) -\left(\frac{x^{2}+y}{x+y^{2}}\right)
  1. Question Prompt: Question Prompt: Calculate the derivative dydx\frac{dy}{dx} for the equation x3+3xy+2y3=17x^{3} + 3xy + 2y^{3} = 17 using implicit differentiation.
  2. Implicit Differentiation: Differentiate both sides of the equation with respect to xx. \newlineddx(x3+3xy+2y3)=ddx(17)\frac{d}{dx}(x^{3} + 3xy + 2y^{3}) = \frac{d}{dx}(17)\newline3x2+3dydxx+3y+6y2dydx=03x^{2} + 3\frac{dy}{dx}x + 3y + 6y^{2}\frac{dy}{dx} = 0
  3. Rearrange for dydx\frac{dy}{dx}: Rearrange to solve for dydx\frac{dy}{dx}.3(dydx)x+6y2(dydx)=3x23y3\left(\frac{dy}{dx}\right)x + 6y^{2}\left(\frac{dy}{dx}\right) = -3x^{2} - 3y(dydx)(3x+6y2)=3x23y\left(\frac{dy}{dx}\right)(3x + 6y^{2}) = -3x^{2} - 3y
  4. Solve for dydx\frac{dy}{dx}: Solve for dydx\frac{dy}{dx}.dydx=(3x2+3y)(3x+6y2)\frac{dy}{dx} = -\frac{(3x^{2} + 3y)}{(3x + 6y^{2})}dydx=(x2+y)(x+2y2)\frac{dy}{dx} = -\frac{(x^{2} + y)}{(x + 2y^{2})}

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