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Popular >

d/(dt)(e^{2t}cos(t))

Solution

\frac{d}{d t} (e^{2 t} cos (t))

Solution

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

Solution steps

\frac{d}{d t} (e^{2 t} cos (t))

Apply the Product Rule:

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

f = e^{2 t}, g = cos (t)

= \frac{d}{d t} (e^{2 t}) cos (t) + \frac{d}{d t} (cos (t)) e^{2 t}

\frac{d}{d t} (e^{2 t}) = e^{2 t} \cdot 2

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

= e^{2 t} \cdot 2 cos (t) + (- sin (t)) e^{2 t}

Simplify

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

Popular Examples

derivative of y=(ln(9x))/(9x)derivative of

y = \frac{ln ( 9 x )}{9 x}

integral from-1 to 7 of (4x+7)-(x^2-2x)

\int_{- 1}^{7} (4 x + 7) - (x^{2} - 2 x) d x

\int 8 t d t

f^'(x)=3e^{2x^2}

f^{^{'}} (x) = 3 e^{2 x^{2}}

y^'=(1-4y^2)/(3xy)

y^{^{'}} = \frac{1 - 4 y ^{2}}{3 x y}

Frequently Asked Questions (FAQ)

What is the d/(dt)(e^{2t}cos(t)) ?
The d/(dt)(e^{2t}cos(t)) is 2e^{2t}cos(t)-e^{2t}sin(t)
What is the first d/(dt)(e^{2t}cos(t)) ?
The first d/(dt)(e^{2t}cos(t)) is 2e^{2t}cos(t)-e^{2t}sin(t)