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Popular >

derivative of e^{13t}sin(t)

Solution

derivative of

e^{13 t} sin (t)

Solution

e^{13 t} \cdot 13 sin (t) + cos (t) e^{13 t}

Solution steps

\frac{d}{d t} (e^{13 t} sin (t))

Apply the Product Rule:

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

f = e^{13 t}, g = sin (t)

= \frac{d}{d t} (e^{13 t}) sin (t) + \frac{d}{d t} (sin (t)) e^{13 t}

\frac{d}{d t} (e^{13 t}) = e^{13 t} \cdot 13

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

= e^{13 t} \cdot 13 sin (t) + cos (t) e^{13 t}

Popular Examples

x(dy)/(dx)+y=6x+1,y(1)=9

x \frac{d y}{d x} + y = 6 x + 1, y (1) = 9

derivative of 4sec(x-5x)

\frac{d}{d x} (4 sec (x) - 5 x)

limit as x approaches 0+of tan^x(7x)

x \to 0 + lim (tan^{x} (7 x))

laplacetransform 5e^{-t}sin(2t)laplace transform

5 e^{- t} sin (2 t)

(\partial)/(\partial x)(sin(pi(5x-4y)))

\frac{\partial}{\partial x} (sin (π (5 x - 4 y)))

Frequently Asked Questions (FAQ)

What is the derivative of e^{13t}sin(t) ?
The derivative of e^{13t}sin(t) is e^{13t}*13sin(t)+cos(t)e^{13t}
What is the first derivative of e^{13t}sin(t) ?
The first derivative of e^{13t}sin(t) is e^{13t}*13sin(t)+cos(t)e^{13t}