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

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

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

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

- sin (x) - cos (y)

Solution steps

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

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

= - sin (x) - cos (y)

\int 5 t^{2} + e^{0.39 t} + 2 d t

\int \frac{t}{a + b t ^{2}} d t

\int 9 e^{- 9 x} d x

sin^{2} (x), sin^{3} (x)

\frac{d}{d x} (sin (\frac{1}{x}) x^{3})

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