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Popular >

derivative of e^tcos(6t)

Solution

derivative of

e^{t} cos (6 t)

Solution

e^{t} cos (6 t) - 6 e^{t} sin (6 t)

Solution steps

\frac{d}{d t} (e^{t} cos (6 t))

Apply the Product Rule:

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

f = e^{t}, g = cos (6 t)

= \frac{d}{d t} (e^{t}) cos (6 t) + \frac{d}{d t} (cos (6 t)) e^{t}

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

\frac{d}{d t} (cos (6 t)) = - sin (6 t) \cdot 6

= e^{t} cos (6 t) + (- sin (6 t) \cdot 6) e^{t}

Simplify

= e^{t} cos (6 t) - 6 e^{t} sin (6 t)

Popular Examples

integral from-3 to 1 of 2e^x

\int_{- 3}^{1} 2 e^{x} d x

limit as x approaches infinity of 0.7x^2

x \to \infty lim (0.7 x^{2})

(\partial)/(\partial x)(x^a(y/x)^{1-a})

\frac{\partial}{\partial x} (x^{a} (\frac{y}{x})^{1 - a})

(\partial)/(\partial y)(ln(y)+2xy^3)

\frac{\partial}{\partial y} (ln (y) + 2 x y^{3})

sum from n=0 to infinity of n!x^n

n = 0 \sum \infty n! x^{n}

Frequently Asked Questions (FAQ)

What is the derivative of e^tcos(6t) ?
The derivative of e^tcos(6t) is e^tcos(6t)-6e^tsin(6t)
What is the first derivative of e^tcos(6t) ?
The first derivative of e^tcos(6t) is e^tcos(6t)-6e^tsin(6t)