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Popular >

derivative of e^tcos(3t)

Solution

derivative of

e^{t} cos (3 t)

Solution

e^{t} cos (3 t) - 3 e^{t} sin (3 t)

Solution steps

\frac{d}{d t} (e^{t} cos (3 t))

Apply the Product Rule:

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

f = e^{t}, g = cos (3 t)

= \frac{d}{d t} (e^{t}) cos (3 t) + \frac{d}{d t} (cos (3 t)) e^{t}

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

\frac{d}{d t} (cos (3 t)) = - sin (3 t) \cdot 3

= e^{t} cos (3 t) + (- sin (3 t) \cdot 3) e^{t}

Simplify

= e^{t} cos (3 t) - 3 e^{t} sin (3 t)

Popular Examples

(\partial)/(\partial y)(x/(1+y))

\frac{\partial}{\partial y} (\frac{x}{1 + y})

y^{''}-10y^'+2y=0

y^{^{''}} - 10 y^{^{'}} + 2 y = 0

(\partial)/(\partial z)(x/(y+z))

\frac{\partial}{\partial z} (\frac{x}{y + z})

laplacetransform 4sin(pit)laplace transform

4 sin (π t)

integral of x^3-3x^{-4}+5

\int x^{3} - 3 x^{- 4} + 5 d x

Frequently Asked Questions (FAQ)

What is the derivative of e^tcos(3t) ?
The derivative of e^tcos(3t) is e^tcos(3t)-3e^tsin(3t)
What is the first derivative of e^tcos(3t) ?
The first derivative of e^tcos(3t) is e^tcos(3t)-3e^tsin(3t)