What is the derivative of-1/64 sin(x/8) ?

The derivative of-1/64 sin(x/8) is -1/512 cos(x/8)

What is the first derivative of-1/64 sin(x/8) ?

The first derivative of-1/64 sin(x/8) is -1/512 cos(x/8)

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\frac{d}{d x} (- \frac{1}{64} sin (\frac{x}{8}))

- \frac{1}{512} cos (\frac{x}{8})

Solution steps

\frac{d}{d x} (- \frac{1}{64} sin (\frac{x}{8}))

Take the constant out:

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

= - \frac{1}{64} \frac{d}{d x} (sin (\frac{x}{8}))

Apply the chain rule:

cos (\frac{x}{8}) \frac{d}{d x} (\frac{x}{8})

= cos (\frac{x}{8}) \frac{d}{d x} (\frac{x}{8})

\frac{d}{d x} (\frac{x}{8}) = \frac{1}{8}

= - \frac{1}{64} cos (\frac{x}{8}) \frac{1}{8}

Simplify

- \frac{1}{64} cos (\frac{x}{8}) \frac{1}{8} : - \frac{1}{512} cos (\frac{x}{8})

= - \frac{1}{512} cos (\frac{x}{8})

What is the derivative of-1/64 sin(x/8) ?
The derivative of-1/64 sin(x/8) is -1/512 cos(x/8)
What is the first derivative of-1/64 sin(x/8) ?
The first derivative of-1/64 sin(x/8) is -1/512 cos(x/8)