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Popular >

derivative of e^tsin(9t)

Solution

derivative of

e^{t} sin (9 t)

Solution

e^{t} sin (9 t) + cos (9 t) \cdot 9 e^{t}

Solution steps

\frac{d}{d t} (e^{t} sin (9 t))

Apply the Product Rule:

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

f = e^{t}, g = sin (9 t)

= \frac{d}{d t} (e^{t}) sin (9 t) + \frac{d}{d t} (sin (9 t)) e^{t}

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

\frac{d}{d t} (sin (9 t)) = cos (9 t) \cdot 9

= e^{t} sin (9 t) + cos (9 t) \cdot 9 e^{t}

Graph

Popular Examples

derivative of sin((pix/2))

\frac{d}{d x} (sin (\frac{π x}{2}))

integral of (3x^2+6x+2)/(x(x+1)^2)

\int \frac{3 x ^{2} + 6 x + 2}{x ( x + 1 ) ^{2}} d x

derivative of x^3+x^{1/2}+2

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

(\partial)/(\partial y)((2x)/(x^2+y^4))

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

tangent of f(x-pi)tangent of

f (x - π)

Frequently Asked Questions (FAQ)

What is the derivative of e^tsin(9t) ?
The derivative of e^tsin(9t) is e^tsin(9t)+cos(9t)*9e^t
What is the first derivative of e^tsin(9t) ?
The first derivative of e^tsin(9t) is e^tsin(9t)+cos(9t)*9e^t