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Popular >

derivative of f(t)=3tsin(pit)

Solution

derivative of

f (t) = 3 t sin (π t)

Solution

3 (sin (π t) + π t cos (π t))

Solution steps

\frac{d}{d t} (3 t sin (π t))

Take the constant out:

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

= 3 \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)

= 3 (\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

= 3 (1 \cdot sin (π t) + cos (π t) π t)

Simplify

= 3 (sin (π t) + π t cos (π t))

Popular Examples

integral of 3x*2^{x^2}

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

limit as x approaches 0 of (sin(x))/(3x)

x \to 0 lim (\frac{sin ( x )}{3 x})

tangent of x^3+y^3=7xy,(2,-4)tangent of

x^{3} + y^{3} = 7 x y, (2, - 4)

tangent of y= 1/(x^2),(-1,1)tangent of

y = \frac{1}{x ^{2}}, (- 1, 1)

integral from 1/5 to 7 of 12xln(5x)

\int_{\frac{1}{5}}^{7} 12 x ln (5 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(t)=3tsin(pit) ?
The derivative of f(t)=3tsin(pit) is 3(sin(pit)+pitcos(pit))
What is the first derivative of f(t)=3tsin(pit) ?
The first derivative of f(t)=3tsin(pit) is 3(sin(pit)+pitcos(pit))