What is the d/(dt)(acos(t),bsin(t),t) ?

The d/(dt)(acos(t),bsin(t),t) is (a,b,((-sin(t))sin(t)t+(tcos(t)+sin(t))cos(t)))

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

The first d/(dt)(acos(t),bsin(t),t) is (a,b,((-sin(t))sin(t)t+(tcos(t)+sin(t))cos(t)))

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\frac{d}{d t} (a cos (t), b sin (t), t)

(a, b, ((- sin (t)) sin (t) t + (t cos (t) + sin (t)) cos (t)))

Solution steps

\frac{d}{d t} (a cos (t), b sin (t), t)

Take the constant out:

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

= (a, b, \frac{d}{d t} (cos (t) sin (t) t))

Apply the Product Rule:

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

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

= (a, b, (\frac{d}{d t} (cos (t)) sin (t) t + \frac{d}{d t} (sin (t) t) cos (t)))

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

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

= (a, b, ((- sin (t)) sin (t) t + (t cos (t) + sin (t)) cos (t)))

\int \frac{e ^{5 x}}{e ^{5 x} + 8} d x

\frac{d}{d x} ((3 x + 1) (5 x - 4))

\frac{\partial}{\partial x} (cos (z w))

n = 1 \sum \infty \frac{n !}{1 0 ^{n}}

\frac{x ^{4} - 5 x ^{3} + x}{x ^{2}}

What is the d/(dt)(acos(t),bsin(t),t) ?
The d/(dt)(acos(t),bsin(t),t) is (a,b,((-sin(t))sin(t)t+(tcos(t)+sin(t))cos(t)))
What is the first d/(dt)(acos(t),bsin(t),t) ?
The first d/(dt)(acos(t),bsin(t),t) is (a,b,((-sin(t))sin(t)t+(tcos(t)+sin(t))cos(t)))