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Popular >

d/(dt)(4e^tcos(t))

Solution

\frac{d}{d t} (4 e^{t} cos (t))

Solution

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

Solution steps

\frac{d}{d t} (4 e^{t} cos (t))

Take the constant out:

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

= 4 \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)

= 4 (\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)

= 4 (e^{t} cos (t) + (- sin (t)) e^{t})

Simplify

= 4 (e^{t} cos (t) - e^{t} sin (t))

Popular Examples

limit as x approaches 0 of (x^3-8)/(x+2)

x \to 0 lim (\frac{x ^{3} - 8}{x + 2})

d/(dt)(sin(4t))

\frac{d}{d t} (sin (4 t))

derivative of f(x)=e-1 derivative of

f (x) = e - 1

-y/(x^2)dx+1/x dy=0

- \frac{y}{x ^{2}} d x + \frac{1}{x} d y = 0

derivative of h(x)=(x-4)(x/2+1)^3 derivative of

h (x) = (x - 4) (\frac{x}{2} + 1)^{3}

Frequently Asked Questions (FAQ)

What is the d/(dt)(4e^tcos(t)) ?
The d/(dt)(4e^tcos(t)) is 4(e^tcos(t)-e^tsin(t))
What is the first d/(dt)(4e^tcos(t)) ?
The first d/(dt)(4e^tcos(t)) is 4(e^tcos(t)-e^tsin(t))