What is the derivative of-8sin((3x/2+1)) ?

The derivative of-8sin((3x/2+1)) is -12cos((3x)/2+1)

What is the first derivative of-8sin((3x/2+1)) ?

The first derivative of-8sin((3x/2+1)) is -12cos((3x)/2+1)

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\frac{d}{d x} (- 8 sin (\frac{3 x}{2} + 1))

- 12 cos (\frac{3 x}{2} + 1)

Solution steps

\frac{d}{d x} (- 8 sin (\frac{3 x}{2} + 1))

Take the constant out:

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

= - 8 \frac{d}{d x} (sin (\frac{3 x}{2} + 1))

Apply the chain rule:

cos (\frac{3 x}{2} + 1) \frac{d}{d x} (\frac{3 x}{2} + 1)

= cos (\frac{3 x}{2} + 1) \frac{d}{d x} (\frac{3 x}{2} + 1)

\frac{d}{d x} (\frac{3 x}{2} + 1) = \frac{3}{2}

= - 8 cos (\frac{3 x}{2} + 1) \frac{3}{2}

Simplify

- 8 cos (\frac{3 x}{2} + 1) \frac{3}{2} : - 12 cos (\frac{3 x}{2} + 1)

= - 12 cos (\frac{3 x}{2} + 1)

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What is the derivative of-8sin((3x/2+1)) ?
The derivative of-8sin((3x/2+1)) is -12cos((3x)/2+1)
What is the first derivative of-8sin((3x/2+1)) ?
The first derivative of-8sin((3x/2+1)) is -12cos((3x)/2+1)