Find dy - dx in the following questions-x2-x y-y2-100

Given, x^2+xy+y^2=100 Differentiating both sides w.r.t. x, we get d/dx(x^2+xy+y^)=0 ⇒ 2x+( xdy/dx+y.1 ) +2ydy/dx=0 (Using product ruled/dx(u.v)=ud/dxv+v ...

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Standard XII

Mathematics

Arithmetic Progression

Find dy / dx ...

Question

Find $\frac{d y}{d x}$ in the following questions:

$x^{2} + x y + y^{2} = 100$

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Solution

Given, $x^{2} + x y + y^{2} = 100$

Differentiating both sides w.r.t. x, we get

$\frac{d}{d x} (x^{2} + x y + y^{)} = 0 \Rightarrow 2 x + (x \frac{d y}{d x} + y .1) + 2 y \frac{d y}{d x} = 0 (U s i n g p r o d u c t r u l e \frac{d}{d x} (u . v) = u \frac{d}{d x} v + v \frac{d}{d x} u)$

$\Rightarrow \frac{d y}{d x} (x + 2 y) = - 2 x - y \Rightarrow \frac{d y}{d x} = - \frac{2 x + y}{x + 2 y}$

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Find dydxin the following questions: x2+xy+y2=100

Given, x2+xy+y2=100 Differentiating both sides w.r.t. x, we get ddx(x2+xy+y)=0 ⇒ 2x+(xdydx+y.1)+2ydydx=0 (Using product ruleddx(u.v)=uddxv+vddxu) ⇒ dydx(x+2y)=−2x−y ⇒ dydx=−2x+yx+2y

Find $\frac{d y}{d x}$ in the following questions:

$x^{2} + x y + y^{2} = 100$