What is implicit (dy)/(dx),5cos(xy)=6x+7y ?

The answer to implicit (dy)/(dx),5cos(xy)=6x+7y is (dy)/(dx)=-(6+5ysin(xy))/(7+5xsin(xy))

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implicit (dy)/(dx),5cos(xy)=6x+7y

implicit derivative

\frac{d y}{d x}, 5 cos (x y) = 6 x + 7 y

\frac{d y}{d x} = - \frac{6 + 5 y sin ( x y )}{7 + 5 x sin ( x y )}

Solution steps

5 cos (x y) = 6 x + 7 y

Treat

y

y (x)

Differentiate both sides:

- 5 sin (x y) (y + x \frac{d y}{d x}) = 6 + 7 \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{6 + 5 y sin ( x y )}{7 + 5 x sin ( x y )}

\frac{d y}{d x} = - \frac{6 + 5 y sin ( x y )}{7 + 5 x sin ( x y )}

What is implicit (dy)/(dx),5cos(xy)=6x+7y ?
The answer to implicit (dy)/(dx),5cos(xy)=6x+7y is (dy)/(dx)=-(6+5ysin(xy))/(7+5xsin(xy))