What is (\partial)/(\partial x)(4sin(2x)) ?

The answer to (\partial)/(\partial x)(4sin(2x)) is 8cos(2x)

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(\partial)/(\partial x)(4sin(2x))

\frac{\partial}{\partial x} (4 sin (2 x))

8 cos (2 x)

Solution steps

\frac{\partial}{\partial x} (4 sin (2 x))

Take the constant out:

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

= 4 \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

= 4 cos (2 x) \cdot 2

Simplify

= 8 cos (2 x)

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What is (\partial)/(\partial x)(4sin(2x)) ?
The answer to (\partial)/(\partial x)(4sin(2x)) is 8cos(2x)