What is (\partial)/(\partial x)(cos(x)-xcos(y)-y) ?

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

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(\partial)/(\partial x)(cos(x)-xcos(y)-y)

\frac{\partial}{\partial x} (cos (x) - x cos (y) - y)

- sin (x) - cos (y)

Solution steps

\frac{\partial}{\partial x} (cos (x) - x cos (y) - y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= - sin (x) - cos (y) - 0

Simplify

= - sin (x) - cos (y)

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

4 x \frac{d y}{d x} = 2 x e^{x} - 4 y + 6 x^{2}

x \to 0 lim (\frac{7}{x} - (\frac{3}{x})^{2})

\frac{d}{d x} ((x + a) e^{2} x + b)

\int x^{2} 2 + x^{3} d x

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