What is (\partial)/(\partial x)(xsin(2y+x)) ?

The answer to (\partial)/(\partial x)(xsin(2y+x)) is sin(2y+x)+xcos(2y+x)

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(\partial)/(\partial x)(xsin(2y+x))

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

sin (2 y + x) + x cos (2 y + x)

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

f = x, g = sin (2 y + x)

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

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

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

= 1 \cdot sin (2 y + x) + cos (2 y + x) x

Simplify

= sin (2 y + x) + x cos (2 y + x)

\frac{d}{d x} (\frac{x - 9}{7 x ^{2} e ^{x}})

\frac{d y}{d x} = \frac{1}{4} e^{x} - \frac{y}{x} + \frac{3 x}{4}

\int \frac{4 - 32 x}{1 - 16 x ^{2}} d x

x^{2} + 4 y^{2} = 4

\frac{d y}{d x}, y = x^{3}

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