What is implicit (dy)/(dx),9cos(xy)=4x+5y ?

The answer to implicit (dy)/(dx),9cos(xy)=4x+5y is (dy)/(dx)=-(4+9ysin(xy))/(5+9xsin(xy))

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implicit (dy)/(dx),9cos(xy)=4x+5y

implicit derivative

\frac{d y}{d x}, 9 cos (x y) = 4 x + 5 y

\frac{d y}{d x} = - \frac{4 + 9 y sin ( x y )}{5 + 9 x sin ( x y )}

Solution steps

9 cos (x y) = 4 x + 5 y

Treat

y

y (x)

Differentiate both sides:

- 9 sin (x y) (y + x \frac{d y}{d x}) = 4 + 5 \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{4 + 9 y sin ( x y )}{5 + 9 x sin ( x y )}

\frac{d y}{d x} = - \frac{4 + 9 y sin ( x y )}{5 + 9 x sin ( x y )}

\int_{- 2}^{2} y^{2} - 2 - y d y

\frac{\partial}{\partial x} (\frac{( x - 3 y )}{x + 3 y})

\int \frac{5 - 50 x}{36 - 25 x ^{2}} d x

\int \frac{x ^{2}}{2} - 2 x d x

\int \frac{1}{( x + 1 ) ( 3 x + 1 )} d x

What is implicit (dy)/(dx),9cos(xy)=4x+5y ?
The answer to implicit (dy)/(dx),9cos(xy)=4x+5y is (dy)/(dx)=-(4+9ysin(xy))/(5+9xsin(xy))