What is the (tcos(t))^' ?

The (tcos(t))^' is cos(t)-tsin(t)

What is the first (tcos(t))^' ?

The first (tcos(t))^' is cos(t)-tsin(t)

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(t cos (t))^{^{'}}

cos (t) - t sin (t)

Solution steps

(t cos (t))^{'}

Apply the Product Rule:

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

f = t, g = cos (t)

= t^{^{'}} cos (t) + (cos (t))^{^{'}} t

t^{'} = 1

(cos (t))^{'} = - sin (t)

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

Simplify

= cos (t) - t sin (t)

\int (x - 1) (x + 2) (x - 3) d x

f (x) = \frac{4 x}{x ^{3} + 5}

\int \frac{80}{64 - x ^{2}} d x

\frac{\partial}{\partial x} (f (x, b, y) (a x + b y))

5 x, \frac{1}{7} x, 50 - x^{2}