What is the derivative of t^8cos(t) ?

The derivative of t^8cos(t) is 8t^7cos(t)-t^8sin(t)

What is the first derivative of t^8cos(t) ?

The first derivative of t^8cos(t) is 8t^7cos(t)-t^8sin(t)

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derivative of

t^{8} cos (t)

8 t^{7} cos (t) - t^{8} sin (t)

Solution steps

\frac{d}{d t} (t^{8} cos (t))

Apply the Product Rule:

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

f = t^{8}, g = cos (t)

= \frac{d}{d t} (t^{8}) cos (t) + \frac{d}{d t} (cos (t)) t^{8}

\frac{d}{d t} (t^{8}) = 8 t^{7}

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

= 8 t^{7} cos (t) + (- sin (t)) t^{8}

Simplify

= 8 t^{7} cos (t) - t^{8} sin (t)

t^{2} \cdot e^{-, at}

f (x) = x (4 - x)^{3}, at x = 2

f (t) = 3 sin (4 t) - 2 e^{2 t}

h (t) = 6 ln (t^{8})

\frac{d}{d x} (144 - x)

What is the derivative of t^8cos(t) ?
The derivative of t^8cos(t) is 8t^7cos(t)-t^8sin(t)
What is the first derivative of t^8cos(t) ?
The first derivative of t^8cos(t) is 8t^7cos(t)-t^8sin(t)