What is (\partial)/(\partial x)(e^xsin(y)-2ysin(x)) ?

The answer to (\partial)/(\partial x)(e^xsin(y)-2ysin(x)) is sin(y)e^x-2ycos(x)

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(\partial)/(\partial x)(e^xsin(y)-2ysin(x))

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

sin (y) e^{x} - 2 y cos (x)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (2 y sin (x)) = 2 y cos (x)

= sin (y) e^{x} - 2 y cos (x)

- \frac{8}{x}

3 x^{2}

\int \frac{1}{( x + 1 ) ^{\frac{3}{2}}} d x

\int π e^{2 x} d x

\int x ln ∣ x ∣ d x

What is (\partial)/(\partial x)(e^xsin(y)-2ysin(x)) ?
The answer to (\partial)/(\partial x)(e^xsin(y)-2ysin(x)) is sin(y)e^x-2ycos(x)