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

The answer to (\partial)/(\partial x)(sin(xy)+x+y) is ycos(xy)+1

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

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

y cos (x y) + 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

= cos (x y) y + 1 + 0

Simplify

= y cos (x y) + 1

\int 1 - sin (2 x) d x

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7 t \frac{d y}{d t} + y = 0, y (1) = 1

\int \frac{c}{x} d x

\int 3 x^{2} - 4 x + 5 d x

What is (\partial)/(\partial x)(sin(xy)+x+y) ?
The answer to (\partial)/(\partial x)(sin(xy)+x+y) is ycos(xy)+1