What is (\partial)/(\partial x)(xsin(x+y)) ?

The answer to (\partial)/(\partial x)(xsin(x+y)) is sin(x+y)+xcos(x+y)

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(\partial)/(\partial x)(xsin(x+y))

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

sin (x + y) + x cos (x + y)

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sin (x + y)

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

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

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

= 1 \cdot sin (x + y) + cos (x + y) x

Simplify

= sin (x + y) + x cos (x + y)

y^{^{'}} + e^{x} y = x^{2} y^{2}

y = x^{2}, y = 17 x

\int_{0}^{1} \frac{e ^{x}}{e ^{x} + 1} d x

\frac{\partial}{\partial x} (a sin (w (x) x) + b cos (w (x) x))

x - x^{\frac{1}{2}}

What is (\partial)/(\partial x)(xsin(x+y)) ?
The answer to (\partial)/(\partial x)(xsin(x+y)) is sin(x+y)+xcos(x+y)