en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of e^{3x}sin(3x)

Solution

\frac{d}{d x} (e^{3 x} sin (3 x))

Solution

e^{3 x} \cdot 3 sin (3 x) + cos (3 x) \cdot 3 e^{3 x}

Solution steps

\frac{d}{d x} (e^{3 x} sin (3 x))

Apply the Product Rule:

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

f = e^{3 x}, g = sin (3 x)

= \frac{d}{d x} (e^{3 x}) sin (3 x) + \frac{d}{d x} (sin (3 x)) e^{3 x}

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

= e^{3 x} \cdot 3 sin (3 x) + cos (3 x) \cdot 3 e^{3 x}

Popular Examples

limit as x approaches infinity of x^2-2

x \to \infty lim (x^{2} - 2)

integral of y^{2/3}

\int y^{\frac{2}{3}} d y

derivative of x^{ln(3x})

\frac{d}{d x} (x^{l n (3 x)})

integral of 25/27 sin^2(x)

\int \frac{25}{27} sin^{2} (x) d x

derivative of 6sec(x-12cos(x))

\frac{d}{d x} (6 sec (x) - 12 cos (x))

Frequently Asked Questions (FAQ)

What is the derivative of e^{3x}sin(3x) ?
The derivative of e^{3x}sin(3x) is e^{3x}*3sin(3x)+cos(3x)*3e^{3x}
What is the first derivative of e^{3x}sin(3x) ?
The first derivative of e^{3x}sin(3x) is e^{3x}*3sin(3x)+cos(3x)*3e^{3x}