What is the d/(dt)(t/(10)sin(5t)) ?

The d/(dt)(t/(10)sin(5t)) is 1/10 (sin(5t)+5tcos(5t))

What is the first d/(dt)(t/(10)sin(5t)) ?

The first d/(dt)(t/(10)sin(5t)) is 1/10 (sin(5t)+5tcos(5t))

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\frac{d}{d t} (\frac{t}{10} sin (5 t))

\frac{1}{10} (sin (5 t) + 5 t cos (5 t))

Solution steps

\frac{d}{d t} (\frac{t}{10} sin (5 t))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{10} \frac{d}{d t} (t sin (5 t))

Apply the Product Rule:

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

f = t, g = sin (5 t)

= \frac{1}{10} (\frac{d t}{d t} sin (5 t) + \frac{d}{d t} (sin (5 t)) t)

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

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

= \frac{1}{10} (1 \cdot sin (5 t) + cos (5 t) \cdot 5 t)

Simplify

= \frac{1}{10} (sin (5 t) + 5 t cos (5 t))

What is the d/(dt)(t/(10)sin(5t)) ?
The d/(dt)(t/(10)sin(5t)) is 1/10 (sin(5t)+5tcos(5t))
What is the first d/(dt)(t/(10)sin(5t)) ?
The first d/(dt)(t/(10)sin(5t)) is 1/10 (sin(5t)+5tcos(5t))