What is the derivative of 3(e^xcos(x)-e^xsin(x)) ?

The derivative of 3(e^xcos(x)-e^xsin(x)) is -6e^xsin(x)

What is the first derivative of 3(e^xcos(x)-e^xsin(x)) ?

The first derivative of 3(e^xcos(x)-e^xsin(x)) is -6e^xsin(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

- 6 e^{x} sin (x)

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

3 (e^{x} cos (x) - e^{x} sin (x) - (e^{x} sin (x) + cos (x) e^{x})) : - 6 e^{x} sin (x)

= - 6 e^{x} sin (x)

x \to 0 lim (\frac{6 x + 4 - 2}{x})

5 e^{- 6 x}

\int \frac{( x ^{4} + 1 )}{x ^{3} + 2 x ^{2} + x} d x

\frac{d}{d x} (- \frac{6}{( x + 1 ) ^{4}})

x \to \infty lim (x \cdot \frac{x}{x})

What is the derivative of 3(e^xcos(x)-e^xsin(x)) ?
The derivative of 3(e^xcos(x)-e^xsin(x)) is -6e^xsin(x)
What is the first derivative of 3(e^xcos(x)-e^xsin(x)) ?
The first derivative of 3(e^xcos(x)-e^xsin(x)) is -6e^xsin(x)