What is (\partial)/(\partial x)((y)(y+sin(y)-x)) ?

The answer to (\partial)/(\partial x)((y)(y+sin(y)-x)) is -y

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(\partial)/(\partial x)((y)(y+sin(y)-x))

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

- y

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= y (0 + 0 - 1)

Simplify

= - y

\frac{2 e ^{- 3 s}}{s ^{2} ( s - 1 ) ( s - 2 )}

(B + BC) (B + B^{^{'}} C) (B + C)

(\frac{x ^{2} - 1}{x ^{2}})^{3}

e^{x} (1 + e^{x})^{10}

- 7.5 + 7.5 (p = 50 - 4 p^{5})

What is (\partial)/(\partial x)((y)(y+sin(y)-x)) ?
The answer to (\partial)/(\partial x)((y)(y+sin(y)-x)) is -y