What is the d/(dt)(sin(8t)) ?

The d/(dt)(sin(8t)) is cos(8t)*8

What is the first d/(dt)(sin(8t)) ?

The first d/(dt)(sin(8t)) is cos(8t)*8

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\frac{d}{d t} (sin (8 t))

cos (8 t) \cdot 8

Solution steps

\frac{d}{d t} (sin (8 t))

Apply the chain rule:

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

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

\frac{d}{d t} (8 t) = 8

= cos (8 t) \cdot 8

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\frac{d}{d x} ((\frac{x - 3}{x + 4}) (x^{2} + 2 x + 1))