What is the derivative of tsin(pit) ?

The derivative of tsin(pit) is sin(pit)+pitcos(pit)

What is the first derivative of tsin(pit) ?

The first derivative of tsin(pit) is sin(pit)+pitcos(pit)

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derivative of

t sin (π t)

sin (π t) + π t cos (π t)

Solution steps

\frac{d}{d t} (t sin (π t))

Apply the Product Rule:

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

f = t, g = sin (π t)

= \frac{d t}{d t} sin (π t) + \frac{d}{d t} (sin (π t)) t

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

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

= 1 \cdot sin (π t) + cos (π t) π t

Simplify

= sin (π t) + π t cos (π t)

\int_{3}^{4.5} \frac{x}{8} d x

\int \frac{x ^{3}}{x ^{3} + 1} d x

\int \frac{4 + x}{x ^{2}} d x

\frac{d q}{d t} = 5 - 5 q

y = lo g_{2} (x) \cdot lo g_{5} (x)

What is the derivative of tsin(pit) ?
The derivative of tsin(pit) is sin(pit)+pitcos(pit)
What is the first derivative of tsin(pit) ?
The first derivative of tsin(pit) is sin(pit)+pitcos(pit)