What is the derivative of f(t)=8tsin(pit) ?

The derivative of f(t)=8tsin(pit) is 8(sin(pit)+pitcos(pit))

What is the first derivative of f(t)=8tsin(pit) ?

The first derivative of f(t)=8tsin(pit) is 8(sin(pit)+pitcos(pit))

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derivative of

f (t) = 8 t sin (π t)

8 (sin (π t) + π t cos (π t))

Solution steps

\frac{d}{d t} (8 t sin (π t))

Take the constant out:

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

= 8 \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)

= 8 (\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

= 8 (1 \cdot sin (π t) + cos (π t) π t)

Simplify

= 8 (sin (π t) + π t cos (π t))

\frac{d}{d x} (x^{2 n})

\frac{d}{d x} (\frac{1}{9 - x ^{2}})

\int_{0}^{t} e^{- 2 x} d x

\int e^{- s t} (t - 2)^{2} d t

\int_{x}^{y} (t^{2} - 1) d t

What is the derivative of f(t)=8tsin(pit) ?
The derivative of f(t)=8tsin(pit) is 8(sin(pit)+pitcos(pit))
What is the first derivative of f(t)=8tsin(pit) ?
The first derivative of f(t)=8tsin(pit) is 8(sin(pit)+pitcos(pit))