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

The answer to implicit (dy)/(dx),sin(x+y)=3x-2y is (dy)/(dx)=(3-cos(x+y))/(cos(x+y)+2)

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

implicit derivative

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

\frac{d y}{d x} = \frac{3 - cos ( x + y )}{cos ( x + y ) + 2}

Solution steps

sin (x + y) = 3 x - 2 y

Treat

y

y (x)

Differentiate both sides:

cos (x + y) (1 + \frac{d y}{d x}) = 3 - 2 \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{3 - cos ( x + y )}{cos ( x + y ) + 2}

\frac{d y}{d x} = \frac{3 - cos ( x + y )}{cos ( x + y ) + 2}

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