What is the d/(dt)(cos(at)) ?

The d/(dt)(cos(at)) is -sin(at)a

What is the first d/(dt)(cos(at)) ?

The first d/(dt)(cos(at)) is -sin(at)a

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

- sin (a t) a

Solution steps

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

Apply the chain rule:

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

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

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

= - sin (a t) a

\frac{d}{d x} ((x - 4)^{8} (2 x + 3)^{6})

y^{^{''}} - 8 y^{^{'}} + 17 y = 0, y (0) = 4

1 - cos (θ)

x \to - 1 lim (- x^{5} - 3 x^{4})

\int 16 x - x^{2} d x