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Popular >

derivative of e^t*sin(2t)

Solution

derivative of

e^{t} \cdot 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

limit as t approaches 2 of sin(pi/4 t)

t \to 2 lim (sin (\frac{π}{4} t))

limit as x approaches 1 of (x^{2n}-2x^n+1)/(x^{2m)-2x^m+1}

x \to 1 lim (\frac{x ^{2 n} - 2 x ^{n} + 1}{x ^{2 m} - 2 x ^{m} + 1})

integral of ((2x^2+3))/(x(x-1)^2)

\int \frac{( 2 x ^{2} + 3 )}{x ( x - 1 ) ^{2}} d x

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

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

(dP)/(dt)=sqrt(Pt),P(1)=2

\frac{d P}{d t} = Pt, P (1) = 2

Frequently Asked Questions (FAQ)

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