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Popular >

derivative of e^tsin(2t)

Solution

derivative of

e^{t} sin (2 t)

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d t} (sin (2 t)) = cos (2 t) \cdot 2

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

Popular Examples

integral from 1 to sqrt(2 of)x2^{(x^2)}

\int_{1}^{2} x 2^{(x^{2})} d x

integral of ((x))/(sqrt(1-x^2))

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

integral from 0 to infinity of x^{-3}

\int_{0}^{\infty} x^{- 3} d x

d/(d{z)}(9{x}^{({y})/({z)}})

\frac{d}{d z} (9 x^{\frac{y}{z}})

integral of (2x+1)e^{x^2+1}

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

Frequently Asked Questions (FAQ)

What is the derivative of e^tsin(2t) ?
The derivative of e^tsin(2t) is e^tsin(2t)+cos(2t)*2e^t
What is the first derivative of e^tsin(2t) ?
The first derivative of e^tsin(2t) is e^tsin(2t)+cos(2t)*2e^t