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

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

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

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

- sin (x)

Solution steps

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

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

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

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

= - sin (x) + 0 - 0

Simplify

= - sin (x)

\frac{d}{d x} (tan (x) + sec (x))

x \to 6 - lim (x + 6)

\int sec (a x) tan (a x) d x

\int \frac{cot ^{2} ( 7 x )}{sec ( 7 x )} d x

\int ln (5 x + 4) d x

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