What is (\partial)/(\partial x)(2xcos(4xy)) ?

The answer to (\partial)/(\partial x)(2xcos(4xy)) is 2(cos(4xy)-4xysin(4xy))

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(\partial)/(\partial x)(2xcos(4xy))

\frac{\partial}{\partial x} (2 x cos (4 x y))

2 (cos (4 x y) - 4 x y sin (4 x y))

Solution steps

\frac{\partial}{\partial x} (2 x cos (4 x y))

Treat

y

as a constant

Take the constant out:

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

= 2 \frac{\partial}{\partial x} (x cos (4 x y))

Apply the Product Rule:

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

f = x, g = cos (4 x y)

= 2 (\frac{\partial}{\partial x} (x) cos (4 x y) + \frac{\partial}{\partial x} (cos (4 x y)) x)

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

\frac{\partial}{\partial x} (cos (4 x y)) = - sin (4 x y) \cdot 4 y

= 2 (1 \cdot cos (4 x y) + (- sin (4 x y) \cdot 4 y) x)

Simplify

= 2 (cos (4 x y) - 4 x y sin (4 x y))

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\int x^{2} (8 x^{3} + 7)^{2} d x

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w \to - 2 lim (\frac{w + 2}{w ^{2} - 6 w - 16})

What is (\partial)/(\partial x)(2xcos(4xy)) ?
The answer to (\partial)/(\partial x)(2xcos(4xy)) is 2(cos(4xy)-4xysin(4xy))