What is the derivative of 7tsin(pit) ?

The derivative of 7tsin(pit) is 7(sin(pit)+pitcos(pit))

What is the first derivative of 7tsin(pit) ?

The first derivative of 7tsin(pit) is 7(sin(pit)+pitcos(pit))

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derivative of

7 t sin (π t)

7 (sin (π t) + π t cos (π t))

Solution steps

\frac{d}{d t} (7 t sin (π t))

Take the constant out:

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

= 7 \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)

= 7 (\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

= 7 (1 \cdot sin (π t) + cos (π t) π t)

Simplify

= 7 (sin (π t) + π t cos (π t))

\frac{\partial}{\partial y} (8 cos (y e^{x y}) sin (x))

\int (sin (θ))^{3} d θ

4 sec (x)

x \to - 9 - lim (\frac{1}{x - 9})

x \to 0 + lim (ln (0))

What is the derivative of 7tsin(pit) ?
The derivative of 7tsin(pit) is 7(sin(pit)+pitcos(pit))
What is the first derivative of 7tsin(pit) ?
The first derivative of 7tsin(pit) is 7(sin(pit)+pitcos(pit))