What is the derivative of ((22.2sin(5t))/t)+44 ?

The derivative of ((22.2sin(5t))/t)+44 is (22.2(5tcos(5t)-sin(5t)))/(t^2)

What is the first derivative of ((22.2sin(5t))/t)+44 ?

The first derivative of ((22.2sin(5t))/t)+44 is (22.2(5tcos(5t)-sin(5t)))/(t^2)

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derivative of

(\frac{22.2 sin ( 5 t )}{t}) + 44

\frac{22.2 ( 5 t cos ( 5 t ) - sin ( 5 t ) )}{t ^{2}}

Solution steps

\frac{d}{d t} (\frac{22.2 sin ( 5 t )}{t} + 44)

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (\frac{22.2 sin ( 5 t )}{t}) + \frac{d}{d t} (44)

\frac{d}{d t} (\frac{22.2 sin ( 5 t )}{t}) = \frac{22.2 ( 5 t cos ( 5 t ) - sin ( 5 t ) )}{t ^{2}}

\frac{d}{d t} (44) = 0

= \frac{22.2 ( 5 t cos ( 5 t ) - sin ( 5 t ) )}{t ^{2}} + 0

Simplify

= \frac{22.2 ( 5 t cos ( 5 t ) - sin ( 5 t ) )}{t ^{2}}

What is the derivative of ((22.2sin(5t))/t)+44 ?
The derivative of ((22.2sin(5t))/t)+44 is (22.2(5tcos(5t)-sin(5t)))/(t^2)
What is the first derivative of ((22.2sin(5t))/t)+44 ?
The first derivative of ((22.2sin(5t))/t)+44 is (22.2(5tcos(5t)-sin(5t)))/(t^2)