What is (\partial)/(\partial x)((e^x-3)sin(y)) ?

The answer to (\partial)/(\partial x)((e^x-3)sin(y)) is e^xsin(y)

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(\partial)/(\partial x)((e^x-3)sin(y))

\frac{\partial}{\partial x} ((e^{x} - 3) sin (y))

e^{x} sin (y)

Solution steps

\frac{\partial}{\partial x} ((e^{x} - 3) sin (y))

Treat

y

as a constant

Take the constant out:

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

= sin (y) \frac{\partial}{\partial x} (e^{x} - 3)

Apply the Sum/Difference Rule:

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

= sin (y) (\frac{\partial}{\partial x} (e^{x}) - \frac{\partial}{\partial x} (3))

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

\frac{\partial}{\partial x} (3) = 0

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

Simplify

= e^{x} sin (y)

What is (\partial)/(\partial x)((e^x-3)sin(y)) ?
The answer to (\partial)/(\partial x)((e^x-3)sin(y)) is e^xsin(y)