What is the derivative of 45+22sin((2pi)/(52)(t-10)) ?

The derivative of 45+22sin((2pi)/(52)(t-10)) is (11pi)/(13)cos((pi(t-10))/(26))

What is the first derivative of 45+22sin((2pi)/(52)(t-10)) ?

The first derivative of 45+22sin((2pi)/(52)(t-10)) is (11pi)/(13)cos((pi(t-10))/(26))

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derivative of

45 + 22 sin (\frac{2 π}{52} (t - 10))

\frac{11 π}{13} cos (\frac{π ( t - 10 )}{26})

Solution steps

\frac{d}{d t} (45 + 22 sin (\frac{2 π}{52} (t - 10)))

Simplify

45 + 22 sin (\frac{2 π}{52} (t - 10)) : 45 + 22 sin (\frac{π ( t - 10 )}{26})

= \frac{d}{d t} (45 + 22 sin (\frac{π ( t - 10 )}{26}))

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (45) + \frac{d}{d t} (22 sin (\frac{π ( t - 10 )}{26}))

\frac{d}{d t} (45) = 0

\frac{d}{d t} (22 sin (\frac{π ( t - 10 )}{26})) = \frac{11 π}{13} cos (\frac{π ( t - 10 )}{26})

= 0 + \frac{11 π}{13} cos (\frac{π ( t - 10 )}{26})

Simplify

= \frac{11 π}{13} cos (\frac{π ( t - 10 )}{26})

What is the derivative of 45+22sin((2pi)/(52)(t-10)) ?
The derivative of 45+22sin((2pi)/(52)(t-10)) is (11pi)/(13)cos((pi(t-10))/(26))
What is the first derivative of 45+22sin((2pi)/(52)(t-10)) ?
The first derivative of 45+22sin((2pi)/(52)(t-10)) is (11pi)/(13)cos((pi(t-10))/(26))