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

The d/(dt)(cos(t)(1-sin(t))) is -sin(t)(1-sin(t))-cos^2(t)

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

The first d/(dt)(cos(t)(1-sin(t))) is -sin(t)(1-sin(t))-cos^2(t)

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\frac{d}{d t} (cos (t) (1 - sin (t)))

- sin (t) (1 - sin (t)) - cos^{2} (t)

Solution steps

\frac{d}{d t} (cos (t) (1 - sin (t)))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (t), g = 1 - sin (t)

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

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

\frac{d}{d t} (1 - sin (t)) = - cos (t)

= (- sin (t)) (1 - sin (t)) + (- cos (t)) cos (t)

Simplify

(- sin (t)) (1 - sin (t)) + (- cos (t)) cos (t) : - sin (t) (1 - sin (t)) - cos^{2} (t)

= - sin (t) (1 - sin (t)) - cos^{2} (t)

What is the d/(dt)(cos(t)(1-sin(t))) ?
The d/(dt)(cos(t)(1-sin(t))) is -sin(t)(1-sin(t))-cos^2(t)
What is the first d/(dt)(cos(t)(1-sin(t))) ?
The first d/(dt)(cos(t)(1-sin(t))) is -sin(t)(1-sin(t))-cos^2(t)