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Popular >

d/(dt)(e^t(cos(t)))

Solution

\frac{d}{d t} (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

derivative of x(ln(x-1))

\frac{d}{d x} (x (ln (x) - 1))

integral from 0 to 3/4 of 1/(9+16x^2)

\int_{0}^{\frac{3}{4}} \frac{1}{9 + 16 x ^{2}} d x

derivative of 1/(sqrt(2pi)e^{-(x^2)/2})

\frac{d}{d x} (\frac{1}{2 π} e^{- \frac{x ^{2}}{2}})

derivative of Ax^2e^x+Bxe^x+Ce^x

\frac{d}{d x} (A x^{2} e^{x} + B x e^{x} + C e^{x})

sum from n=1 to infinity of ((n+1))/(n!)

n = 1 \sum \infty \frac{( n + 1 )}{n !}

Frequently Asked Questions (FAQ)

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