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Popular >

derivative of (t^2+t)cos(5t)

Solution

derivative of

(t^{2} + t) cos (5 t)

Solution

cos (5 t) (2 t + 1) - 5 sin (5 t) (t^{2} + t)

Solution steps

\frac{d}{d t} ((t^{2} + t) cos (5 t))

Apply the Product Rule:

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

f = t^{2} + t, g = cos (5 t)

= \frac{d}{d t} (t^{2} + t) cos (5 t) + \frac{d}{d t} (cos (5 t)) (t^{2} + t)

\frac{d}{d t} (t^{2} + t) = 2 t + 1

\frac{d}{d t} (cos (5 t)) = - sin (5 t) \cdot 5

= (2 t + 1) cos (5 t) + (- sin (5 t) \cdot 5) (t^{2} + t)

Simplify

= cos (5 t) (2 t + 1) - 5 sin (5 t) (t^{2} + t)

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Frequently Asked Questions (FAQ)

What is the derivative of (t^2+t)cos(5t) ?
The derivative of (t^2+t)cos(5t) is cos(5t)(2t+1)-5sin(5t)(t^2+t)
What is the first derivative of (t^2+t)cos(5t) ?
The first derivative of (t^2+t)cos(5t) is cos(5t)(2t+1)-5sin(5t)(t^2+t)