If 3y^(2)+x^(2)y+3=3x then find (dy)/(dx) in terms of x and y. Answer: (dy)/(dx)=

Question

If  3y^(2)+x^(2)y+3=3x then find  (dy)/(dx) in terms of  x and  y. Answer:  (dy)/(dx)=

Bytelearn · Accepted Answer

Given Equation: We are given the equation 3y^2 + x^2y + 3 = 3x, and we need to find the derivative of y with respect to x, which is 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.Implicit Differentiation: First, we differentiate the left side of the equation with respect to x. The derivative of 3y^2 with respect to x is 6y(dy/dx), since y is a function of x and we apply the chain rule. The derivative of x^2y with respect to x is 2xy + x^2(dy/dx), where we use the product rule. The derivative of the constant 3 with respect to x is 0.Differentiate Left Side: Now, we differentiate the right side of the equation with respect to x. The derivative of 3x with respect to x is 3.Differentiate Right Side: We now write the differentiated equation: 6y(dy/dx) + 2xy + x^2(dy/dx) = 3.Write Differentiated Equation: Next, we collect all terms involving (dy/dx) on one side of the equation and the remaining terms on the other side. This gives us 6y(dy/dx) + x^2(dy/dx) = 3 - 2xy.Collect Terms: We factor out (dy/dx) from the left side of the equation to get (dy/dx)(6y + x^2) = 3 - 2xy.Factor Out: To solve for (dy/dx), we divide both sides of the equation by (6y + x^2), which gives us (dy/dx) = (3 - 2xy) / (6y + x^2).

If $3 y^{2}+x^{2} y+3=3 x$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ . $\newline$ Answer: $\frac{d y}{d x}=$

Full solution

More problems from Evaluate functions

Related topics

If 3y2+x2y+3=3x 3 y^{2}+x^{2} y+3=3 x 3y2+x2y+3=3x 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 $3 y^{2}+x^{2} y+3=3 x$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ . $\newline$ Answer: $\frac{d y}{d x}=$