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

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

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(\partial)/(\partial y)((e^x-x)cos(y))

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

- sin (y) (e^{x} - x)

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the common derivative:

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

= (e^{x} - x) (- sin (y))

Simplify

= - sin (y) (e^{x} - x)

\int (sin (x) - 5 cos (x)) d x

x \to 1 lim (\frac{x}{x ^{2} + 1})

\frac{\partial}{\partial x} (e^{- 2 x^{2} - 5 y^{2}})

\int x y e^{x} d x

\int (ln (x + 1 + x^{2}))^{'} d x

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