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

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

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

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

sin (x)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 - (- sin (x))

Simplify

= sin (x)

y = \frac{1}{x}, y = \frac{1}{x ^{2}}, x = 5

\frac{d}{d x} (- 3 x^{4} + 2 y^{2})

\frac{2 x + 1}{4 x ^{2} + 1}

\int x cos (a x) d x

\frac{\partial}{\partial x} (z e^{x yz})

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