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Popular >

derivative of e^tsin(3t)

Solution

derivative of

e^{t} sin (3 t)

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Graph

Popular Examples

integral of sin^6(2x)cos^3(2x)

\int sin^{6} (2 x) cos^{3} (2 x) d x

(\partial)/(\partial x)(xy-z^2+17x^2z)

\frac{\partial}{\partial x} (x y - z^{2} + 17 x^{2} z)

tangent of y=-x^2+4x+2,(3,5)tangent of

y = - x^{2} + 4 x + 2, (3, 5)

(\partial)/(\partial x)(x/(y^3))

\frac{\partial}{\partial x} (\frac{x}{y ^{3}})

(\partial)/(\partial x)(4xsin(6x^2y))

\frac{\partial}{\partial x} (4 x sin (6 x^{2} y))

Frequently Asked Questions (FAQ)

What is the derivative of e^tsin(3t) ?
The derivative of e^tsin(3t) is e^tsin(3t)+cos(3t)*3e^t
What is the first derivative of e^tsin(3t) ?
The first derivative of e^tsin(3t) is e^tsin(3t)+cos(3t)*3e^t