What is the derivative of x=tsin(t) ?

The derivative of x=tsin(t) is sin(t)+tcos(t)

What is the first derivative of x=tsin(t) ?

The first derivative of x=tsin(t) is sin(t)+tcos(t)

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derivative of

x = t sin (t)

sin (t) + t cos (t)

Solution steps

\frac{d}{d t} (t sin (t))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t, g = sin (t)

= \frac{d t}{d t} sin (t) + \frac{d}{d t} (sin (t)) t

\frac{d t}{d t} = 1

\frac{d}{d t} (sin (t)) = cos (t)

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

Simplify

= sin (t) + t cos (t)

8 e^{t}

x \to 0 - lim (x^{2} sin (\frac{1}{x}))

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

t y^{^{'}} = y^{2} + 1

\int x cos (b x) d x

What is the derivative of x=tsin(t) ?
The derivative of x=tsin(t) is sin(t)+tcos(t)
What is the first derivative of x=tsin(t) ?
The first derivative of x=tsin(t) is sin(t)+tcos(t)