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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

n = 1 \sum \infty \frac{n !}{10 3 ^{n}}

f (x) = x + \frac{3}{x}, at x = 2

E

f (x) = e^{- x} - e^{- x} x

x \to 3 + lim (\frac{x + 1}{x - 3})

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