What is the derivative of 7tsin(2t) ?

The derivative of 7tsin(2t) is 7(sin(2t)+2tcos(2t))

What is the first derivative of 7tsin(2t) ?

The first derivative of 7tsin(2t) is 7(sin(2t)+2tcos(2t))

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derivative of

7 t sin (2 t)

7 (sin (2 t) + 2 t cos (2 t))

Solution steps

\frac{d}{d t} (7 t sin (2 t))

Take the constant out:

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

= 7 \frac{d}{d t} (t sin (2 t))

Apply the Product Rule:

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

f = t, g = sin (2 t)

= 7 (\frac{d t}{d t} sin (2 t) + \frac{d}{d t} (sin (2 t)) t)

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

\frac{d}{d t} (sin (2 t)) = cos (2 t) \cdot 2

= 7 (1 \cdot sin (2 t) + cos (2 t) \cdot 2 t)

Simplify

= 7 (sin (2 t) + 2 t cos (2 t))

\frac{d}{d x} (x y e^{\frac{- x ^{2}}{2} - \frac{y ^{2}}{2}})

\int r 9 - r^{2} d r

x^{^{'}} + (2 sin (t) cos (t)) x = e^{- s i n^{2} (t)}

\int ln (r) d r

y^{^{'}} = - 6 x y^{4}

What is the derivative of 7tsin(2t) ?
The derivative of 7tsin(2t) is 7(sin(2t)+2tcos(2t))
What is the first derivative of 7tsin(2t) ?
The first derivative of 7tsin(2t) is 7(sin(2t)+2tcos(2t))