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

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

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

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

cos (x)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= cos (x) - 0

Simplify

= cos (x)

\frac{d}{d x} (arctanh (x))

\frac{1}{3 - 2 x}, 1

f (x) = x^{2} - 3 x

\frac{1}{3 + 2 x}

\frac{1}{1 - x}, 0

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