What is the derivative of pit+cos((4pit+pi)/2) ?

The derivative of pit+cos((4pit+pi)/2) is pi-sin((4pit+pi)/2)*2pi

What is the first derivative of pit+cos((4pit+pi)/2) ?

The first derivative of pit+cos((4pit+pi)/2) is pi-sin((4pit+pi)/2)*2pi

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derivative of

π t + cos (\frac{4 π t + π}{2})

π - sin (\frac{4 π t + π}{2}) \cdot 2 π

Solution steps

\frac{d}{d t} (π t + cos (\frac{4 π t + π}{2}))

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (π t) + \frac{d}{d t} (cos (\frac{4 π t + π}{2}))

\frac{d}{d t} (π t) = π

\frac{d}{d t} (cos (\frac{4 π t + π}{2})) = - sin (\frac{4 π t + π}{2}) \cdot 2 π

= π - sin (\frac{4 π t + π}{2}) \cdot 2 π

What is the derivative of pit+cos((4pit+pi)/2) ?
The derivative of pit+cos((4pit+pi)/2) is pi-sin((4pit+pi)/2)*2pi
What is the first derivative of pit+cos((4pit+pi)/2) ?
The first derivative of pit+cos((4pit+pi)/2) is pi-sin((4pit+pi)/2)*2pi