If 3x+xy+5y=0 then find (dy)/(dx) in terms of x and y. Answer: (dy)/(dx)=

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If  3x+xy+5y=0 then find  (dy)/(dx) in terms of  x and  y. Answer:  (dy)/(dx)=

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Given Equation: We are given the equation 3x + xy + 5y = 0 and we need to find the derivative of y with respect to x, denoted as (dy)/(dx). To do this, we will use implicit differentiation, which involves taking the derivative of both sides of the equation with respect to x, while treating y as a function of x.Differentiate 3x: First, differentiate the term 3x with respect to x. The derivative of 3x with respect to x is 3, since the derivative of x is 1 and the constant 3 remains unchanged.Differentiate xy: Next, differentiate the term xy with respect to x. Since this term is a product of x and y, we use the product rule: (d/dx)(u*v) = u'v + uv', where u = x and v = y. The derivative of x with respect to x is 1, and we denote the derivative of y with respect to x as (dy)/(dx). Therefore, the derivative of xy with respect to x is y + x*(dy)/(dx).Differentiate 5y: Now, differentiate the term 5y with respect to x. Since y is a function of x, the derivative of 5y with respect to x is 5*(dy)/(dx), using the constant multiple rule.Combine Derivatives: Putting it all together, the derivative of the left side of the equation 3x + xy + 5y with respect to x is 3 + y + x*(dy)/(dx) + 5*(dy)/(dx). The derivative of the right side of the equation, which is 0, is simply 0.Isolate (dy)/(dx): Now we have the equation 3 + y + x*(dy)/(dx) + 5*(dy)/(dx) = 0. We need to solve for (dy)/(dx). To do this, we will group the terms containing (dy)/(dx) on one side and the constants on the other side.Factor Out (dy)/(dx): Subtract 3 and y from both sides of the equation to isolate the terms containing (dy)/(dx). This gives us x*(dy)/(dx) + 5*(dy)/(dx) = -3 - y.Solve for (dy)/(dx): Factor out (dy)/(dx) from the left side of the equation to get (dy)/(dx) * (x + 5) = -3 - y.Finally, divide both sides of the equation by (x + 5) to solve for (dy)/(dx). This gives us (dy)/(dx) = (-3 - y) / (x + 5).

If $3 x+x y+5 y=0$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ . $\newline$ Answer: $\frac{d y}{d x}=$

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If 3x+xy+5y=0 3 x+x y+5 y=0 3x+xy+5y=0 then find dydx \frac{d y}{d x} dxdy​ in terms of x x x and y y y.\newlineAnswer: dydx= \frac{d y}{d x}= dxdy​=

If $3 x+x y+5 y=0$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ . $\newline$ Answer: $\frac{d y}{d x}=$