What is the d/(dt)(cos(t)+1) ?

The d/(dt)(cos(t)+1) is -sin(t)

What is the first d/(dt)(cos(t)+1) ?

The first d/(dt)(cos(t)+1) is -sin(t)

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\frac{d}{d t} (cos (t) + 1)

- sin (t)

Solution steps

\frac{d}{d t} (cos (t) + 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (cos (t)) + \frac{d}{d t} (1)

\frac{d}{d t} (cos (t)) = - sin (t)

\frac{d}{d t} (1) = 0

= - sin (t) + 0

Simplify

= - sin (t)

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\int x^{2} (x^{3} + 2)^{4} d x

\int_{0}^{1} x (1 - x)^{2} d x