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

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

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

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

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

Solution steps

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

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))

\frac{d}{d x} (x \cdot cos (y))

x \to 0 lim (\frac{cot ( π x ) sin ( x )}{2 sec ( x )})

\int cos (3 t) d t

\frac{d}{d x} (2 f (x))

\int (e^{- x^{2}})^{2} d x

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