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

The derivative of-e^xsin(x) is -e^xsin(x)-e^xcos(x)

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

The first derivative of-e^xsin(x) is -e^xsin(x)-e^xcos(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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