What is (\partial)/(\partial y)(e^xsin(y)+3y) ?

The answer to (\partial)/(\partial y)(e^xsin(y)+3y) is e^xcos(y)+3

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(\partial)/(\partial y)(e^xsin(y)+3y)

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

e^{x} cos (y) + 3

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (3 y) = 3

= e^{x} cos (y) + 3

\int \frac{1}{x ^{2} + 3 x - 4} d x

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

x \to 0 lim (4 - x)

\frac{\partial}{\partial x} (ln (x y) + ln (yz) + 5 ln (x z))

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

What is (\partial)/(\partial y)(e^xsin(y)+3y) ?
The answer to (\partial)/(\partial y)(e^xsin(y)+3y) is e^xcos(y)+3