What is the d/(dt)(5cos(2t)) ?

The d/(dt)(5cos(2t)) is -10sin(2t)

What is the first d/(dt)(5cos(2t)) ?

The first d/(dt)(5cos(2t)) is -10sin(2t)

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\frac{d}{d t} (5 cos (2 t))

- 10 sin (2 t)

Solution steps

\frac{d}{d t} (5 cos (2 t))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d t} (cos (2 t))

Apply the chain rule:

- sin (2 t) \frac{d}{d t} (2 t)

= - sin (2 t) \frac{d}{d t} (2 t)

\frac{d}{d t} (2 t) = 2

= 5 (- sin (2 t) \cdot 2)

Simplify

= - 10 sin (2 t)

x \to 0 lim (\frac{tan ( x )}{3 x})

f (x) = - 3 x^{2} - 5 x + 1

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