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Popular >

derivative of e^tcos(4t)

Solution

derivative of

e^{t} cos (4 t)

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = e^{t}, g = cos (4 t)

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

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

\frac{d}{d t} (cos (4 t)) = - sin (4 t) \cdot 4

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

Simplify

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

Popular Examples

integral of x^{5/2}ln(x)

\int x^{\frac{5}{2}} ln (x) d x

(\partial)/(\partial x)((3x-2x^2)^3)

\frac{\partial}{\partial x} ((3 x - 2 x^{2})^{3})

integral of ((1+x)/x)^2

\int (\frac{1 + x}{x})^{2} d x

(dy)/(dx)= 1/(y^2)

\frac{d y}{d x} = \frac{1}{y ^{2}}

tangent of f(x)=3x-12x^3,\at x=0 tangent of

f (x) = 3 x - 12 x^{3}, at x = 0

Frequently Asked Questions (FAQ)

What is the derivative of e^tcos(4t) ?
The derivative of e^tcos(4t) is e^tcos(4t)-4e^tsin(4t)
What is the first derivative of e^tcos(4t) ?
The first derivative of e^tcos(4t) is e^tcos(4t)-4e^tsin(4t)