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Popular >

derivative of e^t(cos(t))

Solution

derivative of

e^{t} (cos (t))

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = e^{t}, g = cos (t)

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

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

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

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

Simplify

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

Popular Examples

area x=-2,x=2,y=2x^2+5,y=0 area

x = - 2, x = 2, y = 2 x^{2} + 5, y = 0

derivative of sin(-1(6x+1))derivative of

sin (- 1 (6 x + 1))

inverse oflaplace 2/(s(s+2))inverse laplace

\frac{2}{s ( s + 2 )}

integral of (cos(x))/((sin(x))^3)

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

limit as x approaches-7+of ((-6x))/(x+7)

x \to - 7 + lim (\frac{( - 6 x )}{x + 7})

Frequently Asked Questions (FAQ)

What is the derivative of e^t(cos(t)) ?
The derivative of e^t(cos(t)) is e^tcos(t)-e^tsin(t)
What is the first derivative of e^t(cos(t)) ?
The first derivative of e^t(cos(t)) is e^tcos(t)-e^tsin(t)