What is the derivative of 3+0.35sin((360t)/(4.5)) ?

The derivative of 3+0.35sin((360t)/(4.5)) is 28cos(80t)

What is the first derivative of 3+0.35sin((360t)/(4.5)) ?

The first derivative of 3+0.35sin((360t)/(4.5)) is 28cos(80t)

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derivative of

3 + 0.35 sin (\frac{360 t}{4.5})

28 cos (80 t)

Solution steps

\frac{d}{d t} (3 + 0.35 sin (\frac{360 t}{4.5}))

Simplify

3 + 0.35 sin (\frac{360 t}{4.5}) : 3 + 0.35 sin (80 t)

= \frac{d}{d t} (3 + 0.35 sin (80 t))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (3) + \frac{d}{d t} (0.35 sin (80 t))

\frac{d}{d t} (3) = 0

\frac{d}{d t} (0.35 sin (80 t)) = 28 cos (80 t)

= 0 + 28 cos (80 t)

Simplify

= 28 cos (80 t)

x - a

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What is the derivative of 3+0.35sin((360t)/(4.5)) ?
The derivative of 3+0.35sin((360t)/(4.5)) is 28cos(80t)
What is the first derivative of 3+0.35sin((360t)/(4.5)) ?
The first derivative of 3+0.35sin((360t)/(4.5)) is 28cos(80t)