What is (\partial)/(\partial x)(4cos(4x)) ?

The answer to (\partial)/(\partial x)(4cos(4x)) is -16sin(4x)

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(\partial)/(\partial x)(4cos(4x))

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

- 16 sin (4 x)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (4 x) = 4

= 4 (- sin (4 x) \cdot 4)

Simplify

= - 16 sin (4 x)

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y^{^{''}} + 8 y^{^{'}} = - 256 cos (8 x)

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What is (\partial)/(\partial x)(4cos(4x)) ?
The answer to (\partial)/(\partial x)(4cos(4x)) is -16sin(4x)