What is the d/(dt)(tsin(pit)) ?

The d/(dt)(tsin(pit)) is sin(pit)+pitcos(pit)

What is the first d/(dt)(tsin(pit)) ?

The first d/(dt)(tsin(pit)) is sin(pit)+pitcos(pit)

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\frac{d}{d t} (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 \frac{1}{t ^{2}} cos (\frac{1}{t} - 1) d t

y = \frac{4}{x ^{5}}

f (x) = 2 x^{3} ln (x)

\int \frac{1}{a ^{2} + v ^{2}} d v

\frac{d}{d x} (\frac{3}{4} x^{\frac{4}{3}})

What is the d/(dt)(tsin(pit)) ?
The d/(dt)(tsin(pit)) is sin(pit)+pitcos(pit)
What is the first d/(dt)(tsin(pit)) ?
The first d/(dt)(tsin(pit)) is sin(pit)+pitcos(pit)