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

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

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

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

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

- sin (t)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= 0 - sin (t)

Simplify

= - sin (t)

- 2 y^{^{'}} + \frac{4 y}{x} = \frac{y ^{3}}{x}

\frac{d}{d t} (\frac{1}{t ^{2}})

\int \frac{5 x - 1}{( 2 x + 1 ) ( x - 1 )} d x

f (x) = arctan (3 x)

\frac{d y}{d t} = k y (100 - y)