What is implicit (dy)/(dx),x=cos(2y) ?

The answer to implicit (dy)/(dx),x=cos(2y) is (dy)/(dx)=-1/(2sin(2y))

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implicit (dy)/(dx),x=cos(2y)

implicit derivative

\frac{d y}{d x}, x = cos (2 y)

\frac{d y}{d x} = - \frac{1}{2 sin ( 2 y )}

Solution steps

x = cos (2 y)

Treat

y

y (x)

Differentiate both sides:

1 = - sin (2 y) \cdot 2 \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{1}{2 sin ( 2 y )}

\frac{d y}{d x} = - \frac{1}{2 sin ( 2 y )}

x \to 0 lim (\frac{5}{2} x^{2})

\int sin (x) sin (\frac{2 x}{3}) d x

\frac{d}{d x} (e^{a (e^{x} - 1)})

\frac{1}{s}

y = 27 - x^{2}, y = 6 x, y = \frac{2}{5} x

What is implicit (dy)/(dx),x=cos(2y) ?
The answer to implicit (dy)/(dx),x=cos(2y) is (dy)/(dx)=-1/(2sin(2y))