What is the derivative of f(t)=6tsin(pit) ?

The derivative of f(t)=6tsin(pit) is 6(sin(pit)+pitcos(pit))

What is the first derivative of f(t)=6tsin(pit) ?

The first derivative of f(t)=6tsin(pit) is 6(sin(pit)+pitcos(pit))

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derivative of

f (t) = 6 t sin (π t)

6 (sin (π t) + π t cos (π t))

Solution steps

\frac{d}{d t} (6 t sin (π t))

Take the constant out:

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

= 6 \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)

= 6 (\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

= 6 (1 \cdot sin (π t) + cos (π t) π t)

Simplify

= 6 (sin (π t) + π t cos (π t))

(\frac{y}{x} + 9 x) d x + (ln (x) - 4) d y = 0

\frac{\partial}{\partial x} (x^{2} + 3 x y + y^{2})

y^{^{''}} - 16 y^{^{'}} + 64 y = 0

\frac{d}{d x} (ln (\frac{( x + 2 ) e ^{3 x}}{x ^{2} + 1}))

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

What is the derivative of f(t)=6tsin(pit) ?
The derivative of f(t)=6tsin(pit) is 6(sin(pit)+pitcos(pit))
What is the first derivative of f(t)=6tsin(pit) ?
The first derivative of f(t)=6tsin(pit) is 6(sin(pit)+pitcos(pit))