What is (\partial)/(\partial x)(e^x-2-cos(xy)) ?

The answer to (\partial)/(\partial x)(e^x-2-cos(xy)) is ysin(xy)+e^x

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(\partial)/(\partial x)(e^x-2-cos(xy))

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (e^{x}) = e^{x}

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

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

= e^{x} - 0 - (- sin (x y) y)

Simplify

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

What is (\partial)/(\partial x)(e^x-2-cos(xy)) ?
The answer to (\partial)/(\partial x)(e^x-2-cos(xy)) is ysin(xy)+e^x