What is the derivative of 2e^3tsin(2t) ?

The derivative of 2e^3tsin(2t) is 2e^3(sin(2t)+2tcos(2t))

What is the first derivative of 2e^3tsin(2t) ?

The first derivative of 2e^3tsin(2t) is 2e^3(sin(2t)+2tcos(2t))

derivative of

2 e^{3} t sin (2 t)

2 e^{3} (sin (2 t) + 2 t cos (2 t))

Solution steps

\frac{d}{d t} (2 e^{3} t sin (2 t))

Take the constant out:

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

= 2 e^{3} \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)

= 2 e^{3} (\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

= 2 e^{3} (1 \cdot sin (2 t) + cos (2 t) \cdot 2 t)

Simplify

= 2 e^{3} (sin (2 t) + 2 t cos (2 t))

d er i v a t i v e tan (e^{s}) in x^{2}

d er i v a t i v e (1 + x)^{2 y + 1}

d er i v a t i v e y = (sin (x))^{5}

d er i v a t i v e 2 - cos^{2} (x)

d er i v a t i v e \frac{tanh ( 4 x + 1 )}{5}

What is the derivative of 2e^3tsin(2t) ?
The derivative of 2e^3tsin(2t) is 2e^3(sin(2t)+2tcos(2t))
What is the first derivative of 2e^3tsin(2t) ?
The first derivative of 2e^3tsin(2t) is 2e^3(sin(2t)+2tcos(2t))