What is (\partial)/(\partial x)(1/y-2xsin(y)) ?

The answer to (\partial)/(\partial x)(1/y-2xsin(y)) is -2sin(y)

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(\partial)/(\partial x)(1/y-2xsin(y))

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

- 2 sin (y)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (\frac{1}{y}) = 0

\frac{\partial}{\partial x} (2 x sin (y)) = 2 sin (y)

= 0 - 2 sin (y)

Simplify

= - 2 sin (y)

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

y^{^{''}} - y^{^{'}} - 2 y = - 2 t + 6 t^{2}

\frac{d}{d x} (e^{s i n^{2} (x)})

y = \frac{2}{x}, y = 8 x, y = \frac{1}{2} x

\frac{d}{d x} (\frac{3}{4 ( 2 x - 5 ) ^{8}})

What is (\partial)/(\partial x)(1/y-2xsin(y)) ?
The answer to (\partial)/(\partial x)(1/y-2xsin(y)) is -2sin(y)