What is implicit (dy)/(dx),x^2=((3x+5y))/(3x-5y) ?

The answer to implicit (dy)/(dx),x^2=((3x+5y))/(3x-5y) is (dy)/(dx)=(x(3x-5y)^2+15y)/(15x)

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implicit (dy)/(dx),x^2=((3x+5y))/(3x-5y)

implicit derivative

\frac{d y}{d x}, x^{2} = \frac{( 3 x + 5 y )}{3 x - 5 y}

\frac{d y}{d x} = \frac{x ( 3 x - 5 y ) ^{2} + 15 y}{15 x}

Solution steps

x^{2} = \frac{3 x + 5 y}{3 x - 5 y}

Treat

y

y (x)

Differentiate both sides:

2 x = \frac{30 x \frac{d y}{d x} - 30 y}{( 3 x - 5 y ) ^{2}}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{x ( 3 x - 5 y ) ^{2} + 15 y}{15 x}

\frac{d y}{d x} = \frac{x ( 3 x - 5 y ) ^{2} + 15 y}{15 x}

What is implicit (dy)/(dx),x^2=((3x+5y))/(3x-5y) ?
The answer to implicit (dy)/(dx),x^2=((3x+5y))/(3x-5y) is (dy)/(dx)=(x(3x-5y)^2+15y)/(15x)