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Popular Calculus >

derivative of f(t)=tsin(pit)

Solution

derivative of

f (t) = t sin (π t)

Solution

sin (π t) + π t cos (π t)

Solution steps

\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)

= \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

= 1 \cdot sin (π t) + cos (π t) π t

Simplify

= sin (π t) + π t cos (π t)

Graph

Popular Examples

integral of x^2tan(x^3)

\int x^{2} tan (x^{3}) d x

(d^2)/(dx^2)(5cos(2x+10))

\frac{d ^{2}}{d x ^{2}} (5 cos (2 x + 10))

limit as q approaches 18 of 0.9q^2-6q+80

q \to 18 lim (0.9 q^{2} - 6 q + 80)

derivative of sec(θ)(θ-tan(θ))

d er i v a t i v e sec (θ) (θ - tan (θ))

f(x)=sqrt(x^2-10x+34)+sqrt(x^2+16)

f (x) = x^{2} - 10 x + 34 + x^{2} + 16

Frequently Asked Questions (FAQ)

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