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

The derivative of xsin(e^x) is sin(e^x)+e^xxcos(e^x)

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

The first derivative of xsin(e^x) is sin(e^x)+e^xxcos(e^x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

sin (e^{x}) + e^{x} x cos (e^{x})

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot sin (e^{x}) + cos (e^{x}) e^{x} x

Simplify

= sin (e^{x}) + e^{x} x cos (e^{x})

\frac{d y}{d x} + 2 y = 3, y (0) = 1

f (x) = x^{4} + 8 x

\frac{d}{d x} (\frac{g ( x )}{h ( x )})

f (x) = 4 x - 8

\int 9 x cos (3 x) d x

What is the derivative of xsin(e^x) ?
The derivative of xsin(e^x) is sin(e^x)+e^xxcos(e^x)
What is the first derivative of xsin(e^x) ?
The first derivative of xsin(e^x) is sin(e^x)+e^xxcos(e^x)