What is the derivative of 5cos(pit) ?

The derivative of 5cos(pit) is -5pisin(pit)

What is the first derivative of 5cos(pit) ?

The first derivative of 5cos(pit) is -5pisin(pit)

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derivative of

5 cos (π t)

- 5 π sin (π t)

Solution steps

\frac{d}{d t} (5 cos (π t))

Take the constant out:

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

= 5 \frac{d}{d t} (cos (π t))

Apply the chain rule:

- sin (π t) \frac{d}{d t} (π t)

= - sin (π t) \frac{d}{d t} (π t)

\frac{d}{d t} (π t) = π

= 5 (- sin (π t) π)

Simplify

= - 5 π sin (π t)

What is the derivative of 5cos(pit) ?
The derivative of 5cos(pit) is -5pisin(pit)
What is the first derivative of 5cos(pit) ?
The first derivative of 5cos(pit) is -5pisin(pit)