Question #cde8d

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Question #cde8d

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Answer 1 · 2017-09-29T03:51:21

$\frac{d y}{d x} = - \frac{16 x^{2} + 15 y}{15 x + 6 y}$ $dy/dx=-(16x^2+15y)/(15x+6y)$

Explanation:

$8 x^{2} + 15 x y + 3 y^{2} = 15$ $8x^2+15xy+3y^2=15$
Differentiating w.r.t. x,
$16 x^{2} + 15 y + 15 x (\frac{d y}{d x}) + 6 y (\frac{d y}{d x}) = 0$ $16x^2+15y+15x(dy/dx)+6y(dy/dx)=0$
$16 x^{2} + 15 y + (\frac{d y}{d x}) (15 x + 6 y) = 0$ $16x^2+15y+(dy /dx)(15x+6y)=0$

Answer 2 · 2017-09-29T10:11:03

$\frac{d y}{d x} = - \frac{16 x + 15 y}{15 x + 6 y}$ $dy/dx=-(16x+15y)/(15x+6y)$

Explanation:

$differentiate implicitly with respect to x$ $"differentiate "color(blue)"implicitly with respect to x"$

$differentiate 15 x y using the product rule$ $"differentiate "15xy" using the "color(blue)"product rule"$

$\Rightarrow 16 x + 15 (x \frac{d y}{d x} + y) + 6 y \frac{d y}{d x} = 0$ $rArr16x+15(xdy/dx+y)+6ydy/dx=0$

$\Rightarrow 16 x + 15 x \frac{d y}{d x} + 15 y + 6 y \frac{d y}{d x} = 0$ $rArr16x+15xdy/dx+15y+6ydy/dx=0$

$\Rightarrow \frac{d y}{d x} (15 x + 6 y) = - 16 x - 15 y$ $rArrdy/dx(15x+6y)=-16x-15y$

$\Rightarrow \frac{d y}{d x} = - \frac{16 x + 15 y}{15 x + 6 y}$ $rArrdy/dx=-(16x+15y)/(15x+6y)$

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