What is the derivative of e^xsin(10x) ?

The derivative of e^xsin(10x) is e^xsin(10x)+cos(10x)*10e^x

What is the first derivative of e^xsin(10x) ?

The first derivative of e^xsin(10x) is e^xsin(10x)+cos(10x)*10e^x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

e^{x} sin (10 x)

e^{x} sin (10 x) + cos (10 x) \cdot 10 e^{x}

Solution steps

\frac{d}{d x} (e^{x} sin (10 x))

Apply the Product Rule:

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

f = e^{x}, g = sin (10 x)

= \frac{d}{d x} (e^{x}) sin (10 x) + \frac{d}{d x} (sin (10 x)) e^{x}

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

\frac{d}{d x} (sin (10 x)) = cos (10 x) \cdot 10

= e^{x} sin (10 x) + cos (10 x) \cdot 10 e^{x}

What is the derivative of e^xsin(10x) ?
The derivative of e^xsin(10x) is e^xsin(10x)+cos(10x)*10e^x
What is the first derivative of e^xsin(10x) ?
The first derivative of e^xsin(10x) is e^xsin(10x)+cos(10x)*10e^x