en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

d/(dt)(e^tcos(t)-e^tsin(t))

Solution

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

Solution

- 2 e^{t} sin (t)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

e^{t} cos (t) - e^{t} sin (t) - (e^{t} sin (t) + cos (t) e^{t}) : - 2 e^{t} sin (t)

= - 2 e^{t} sin (t)

Popular Examples

(\partial}{\partial x}(\frac{K(x))/4 (10L-L^2))

\frac{\partial}{\partial x} (\frac{K ( x )}{4} (10 L - L^{2}))

area y=5x,y= 1/4 x,y=66-x^2 area

y = 5 x, y = \frac{1}{4} x, y = 66 - x^{2}

integral of (sec(x)tan(x))/(sec(x)-8)

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 8} d x

derivative of cos(3x+sin(3x))

\frac{d}{d x} (cos (3 x) + sin (3 x))

y^{''}-3y^'+2y=2e^{3t}

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 e^{3 t}

Frequently Asked Questions (FAQ)

What is the d/(dt)(e^tcos(t)-e^tsin(t)) ?
The d/(dt)(e^tcos(t)-e^tsin(t)) is -2e^tsin(t)
What is the first d/(dt)(e^tcos(t)-e^tsin(t)) ?
The first d/(dt)(e^tcos(t)-e^tsin(t)) is -2e^tsin(t)