What is (\partial)/(\partial x)(2xy+sin(x)) ?

The answer to (\partial)/(\partial x)(2xy+sin(x)) is 2y+cos(x)

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(\partial)/(\partial x)(2xy+sin(x))

\frac{\partial}{\partial x} (2 x y + sin (x))

2 y + cos (x)

Solution steps

\frac{\partial}{\partial x} (2 x y + sin (x))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 y + cos (x)

What is (\partial)/(\partial x)(2xy+sin(x)) ?
The answer to (\partial)/(\partial x)(2xy+sin(x)) is 2y+cos(x)