What is the d/(dt)(acos(3t)) ?

The d/(dt)(acos(3t)) is -3asin(3t)

What is the first d/(dt)(acos(3t)) ?

The first d/(dt)(acos(3t)) is -3asin(3t)

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\frac{d}{d t} (a cos (3 t))

- 3 a sin (3 t)

Solution steps

\frac{d}{d t} (a cos (3 t))

Take the constant out:

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

= a \frac{d}{d t} (cos (3 t))

Apply the chain rule:

- sin (3 t) \frac{d}{d t} (3 t)

= - sin (3 t) \frac{d}{d t} (3 t)

\frac{d}{d t} (3 t) = 3

= a (- sin (3 t) \cdot 3)

Simplify

= - 3 a sin (3 t)

\frac{\partial}{\partial x} (e^{3 x^{2}} + 4 x y + 5 y^{2})

f (t) = t e^{t}

f (x) = cos (\frac{π x}{2}), at x = 0.7

x y d x - (x^{2} - x) d y = 0

\frac{\partial}{\partial x} (sin (x y) + cos (x y))