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Popular Calculus >

derivative of f(t)=e^{9tsin(2t)}

Solution

derivative of

f (t) = e^{9 t s i n (2 t)}

Solution

e^{9 t s i n (2 t)} \cdot 9 (sin (2 t) + 2 t cos (2 t))

Solution steps

\frac{d}{d t} (e^{9 t s i n (2 t)})

Apply the chain rule:

e^{9 t s i n (2 t)} \frac{d}{d t} (9 t sin (2 t))

= e^{9 t s i n (2 t)} \frac{d}{d t} (9 t sin (2 t))

\frac{d}{d t} (9 t sin (2 t)) = 9 (sin (2 t) + 2 t cos (2 t))

= e^{9 t s i n (2 t)} \cdot 9 (sin (2 t) + 2 t cos (2 t))

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(t)=e^{9tsin(2t)} ?
The derivative of f(t)=e^{9tsin(2t)} is e^{9tsin(2t)}*9(sin(2t)+2tcos(2t))
What is the first derivative of f(t)=e^{9tsin(2t)} ?
The first derivative of f(t)=e^{9tsin(2t)} is e^{9tsin(2t)}*9(sin(2t)+2tcos(2t))