What is (\partial)/(\partial y)(z-xsin(y)-4) ?

The answer to (\partial)/(\partial y)(z-xsin(y)-4) is -xcos(y)

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(\partial)/(\partial y)(z-xsin(y)-4)

\frac{\partial}{\partial y} (z - x sin (y) - 4)

- x cos (y)

Solution steps

\frac{\partial}{\partial y} (z - x sin (y) - 4)

Treat

z, x

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (z) - \frac{\partial}{\partial y} (x sin (y)) - \frac{\partial}{\partial y} (4)

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

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

\frac{\partial}{\partial y} (4) = 0

= 0 - x cos (y) - 0

Simplify

= - x cos (y)

x \to - 1 lim (1 - 2 x)

\int e^{x} ln (1 + e^{x}) d x

(2 x - 1) d x + (7 y + 9) d y = 0

(x^{3 x})^{^{'}}

(1 + cos (x)) y^{^{'}} = (1 + e^{- y}) sin (x)

What is (\partial)/(\partial y)(z-xsin(y)-4) ?
The answer to (\partial)/(\partial y)(z-xsin(y)-4) is -xcos(y)