What is (\partial)/(\partial x)(3sin(2x)cos(6y)) ?

The answer to (\partial)/(\partial x)(3sin(2x)cos(6y)) is 6cos(2x)cos(6y)

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(\partial)/(\partial x)(3sin(2x)cos(6y))

\frac{\partial}{\partial x} (3 sin (2 x) cos (6 y))

6 cos (2 x) cos (6 y)

Solution steps

\frac{\partial}{\partial x} (3 sin (2 x) cos (6 y))

Treat

y

as a constant

Take the constant out:

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

= 3 cos (6 y) \frac{\partial}{\partial x} (sin (2 x))

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (2 x) = 2

= 3 cos (6 y) cos (2 x) \cdot 2

Simplify

= 6 cos (2 x) cos (6 y)

\frac{\partial}{\partial x} (ln (1 - x))

\int (1 + t) d t

\frac{1 + x}{1 - x}

\frac{\partial}{\partial x} (7 x e^{x y})

\int_{0}^{3} 3 e^{- 2 x} d x

What is (\partial)/(\partial x)(3sin(2x)cos(6y)) ?
The answer to (\partial)/(\partial x)(3sin(2x)cos(6y)) is 6cos(2x)cos(6y)