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

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

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(\partial)/(\partial x)(x*sin(y+2x))

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\frac{d}{d x} (x^{9} e^{8 x})

e^{3 t}

\frac{d y}{d x} = \frac{( 3 x + 2 y + \frac{1}{3} ) ^{2}}{3 x + 2 y + \frac{1}{3}}

x \to + 2 + lim (5)

\int_{0}^{\frac{π}{6}} cos^{2} (x) d x

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