What is the derivative of (t+1)cos(-t) ?

The derivative of (t+1)cos(-t) is -sin(t)(1+t)+cos(t)

What is the first derivative of (t+1)cos(-t) ?

The first derivative of (t+1)cos(-t) is -sin(t)(1+t)+cos(t)

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derivative of

(t + 1) cos (- t)

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

Solution steps

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

Simplify

(t + 1) cos (- t) : cos (t) (1 + t)

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

Apply the Product Rule:

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

f = cos (t), g = 1 + t

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

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

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

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

Simplify

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

What is the derivative of (t+1)cos(-t) ?
The derivative of (t+1)cos(-t) is -sin(t)(1+t)+cos(t)
What is the first derivative of (t+1)cos(-t) ?
The first derivative of (t+1)cos(-t) is -sin(t)(1+t)+cos(t)