What is the derivative of tcos(t) ?

The derivative of tcos(t) is cos(t)-tsin(t)

What is the first derivative of tcos(t) ?

The first derivative of tcos(t) is cos(t)-tsin(t)

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derivative of

t cos (t)

cos (t) - t sin (t)

Solution steps

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

Apply the Product Rule:

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

f = t, g = cos (t)

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

\frac{d t}{d t} = 1

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

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

Simplify

= cos (t) - t sin (t)

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

\frac{d}{d x} (64 e^{- 4 x})

\frac{\partial}{\partial y} (\frac{x y}{x ^{2} - y ^{2}})

y = 4 x, x = 4, x = 9

x \to + 0 lim (\frac{1}{x} cos (\frac{1}{x}))

What is the derivative of tcos(t) ?
The derivative of tcos(t) is cos(t)-tsin(t)
What is the first derivative of tcos(t) ?
The first derivative of tcos(t) is cos(t)-tsin(t)