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

The answer to (\partial)/(\partial x)(xcos(y)-ycos(x)) is cos(y)+ysin(x)

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

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

cos (y) + y sin (x)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= cos (y) + y sin (x)

g (x) = ln (x e^{- 2 x})

\int \frac{x ^{4} + 10 x ^{3}}{2 x ^{2}} d x

\int 2 (1 - 3 x)^{2} d x

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

\int \frac{1}{e ^{- x} + e ^{x}} d x

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