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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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