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Popular >

d/(dt)(9tsin(pit))

Solution

\frac{d}{d t} (9 t sin (π t))

Solution

9 (sin (π t) + π t cos (π t))

Solution steps

\frac{d}{d t} (9 t sin (π t))

Take the constant out:

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

= 9 \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)

= 9 (\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

= 9 (1 \cdot sin (π t) + cos (π t) π t)

Simplify

= 9 (sin (π t) + π t cos (π t))

Popular Examples

integral of x^3sqrt(x^2-3)

\int x^{3} x^{2} - 3 d x

limit as x approaches infinity of 8xe^{1/x}-8x

x \to \infty lim (8 x e^{\frac{1}{x}} - 8 x)

integral of (x^2+x)^7(2x+1)

\int (x^{2} + x)^{7} (2 x + 1) d x

integral from 0 to 1 of e^x-e^{-x}

\int_{0}^{1} e^{x} - e^{- x} d x

tangent of f(x)=e^x(9-3x+2x^2),\at x=0 tangent of

f (x) = e^{x} (9 - 3 x + 2 x^{2}), at x = 0

Frequently Asked Questions (FAQ)

What is the d/(dt)(9tsin(pit)) ?
The d/(dt)(9tsin(pit)) is 9(sin(pit)+pitcos(pit))
What is the first d/(dt)(9tsin(pit)) ?
The first d/(dt)(9tsin(pit)) is 9(sin(pit)+pitcos(pit))