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))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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))

6 x^{4} - 7 x^{2} + 9

3 x + y^{2}

tan (e^{s}) in x^{2}

(1 + x)^{2 y + 1}

y = (sin (x))^{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))