What is (\partial)/(\partial y)(cos(xy)-e^z+2) ?

The answer to (\partial)/(\partial y)(cos(xy)-e^z+2) is -xsin(xy)

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(\partial)/(\partial y)(cos(xy)-e^z+2)

\frac{\partial}{\partial y} (cos (x y) - e^{z} + 2)

- x sin (x y)

Solution steps

\frac{\partial}{\partial y} (cos (x y) - e^{z} + 2)

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (cos (x y)) - \frac{\partial}{\partial y} (e^{z}) + \frac{\partial}{\partial y} (2)

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

\frac{\partial}{\partial y} (e^{z}) = 0

\frac{\partial}{\partial y} (2) = 0

= - sin (x y) x - 0 + 0

Simplify

= - x sin (x y)

\frac{\partial}{\partial y} (r cos (y))

\frac{d}{d x} (4 x^{2} - 5 x + 4)

f (x) = x^{4 c o s (x)}

n \to \infty lim (- 1 0^{n})

x \to - 3 lim (\frac{x}{x + 5})

What is (\partial)/(\partial y)(cos(xy)-e^z+2) ?
The answer to (\partial)/(\partial y)(cos(xy)-e^z+2) is -xsin(xy)