What is the derivative of t^9cos(t) ?

The derivative of t^9cos(t) is 9t^8cos(t)-t^9sin(t)

What is the first derivative of t^9cos(t) ?

The first derivative of t^9cos(t) is 9t^8cos(t)-t^9sin(t)

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derivative of

t^{9} cos (t)

9 t^{8} cos (t) - t^{9} sin (t)

Solution steps

\frac{d}{d t} (t^{9} cos (t))

Apply the Product Rule:

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

f = t^{9}, g = cos (t)

= \frac{d}{d t} (t^{9}) cos (t) + \frac{d}{d t} (cos (t)) t^{9}

\frac{d}{d t} (t^{9}) = 9 t^{8}

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

= 9 t^{8} cos (t) + (- sin (t)) t^{9}

Simplify

= 9 t^{8} cos (t) - t^{9} sin (t)

What is the derivative of t^9cos(t) ?
The derivative of t^9cos(t) is 9t^8cos(t)-t^9sin(t)
What is the first derivative of t^9cos(t) ?
The first derivative of t^9cos(t) is 9t^8cos(t)-t^9sin(t)