What is the derivative of f(t)=e^{5tsin(2t)} ?

The derivative of f(t)=e^{5tsin(2t)} is e^{5tsin(2t)}*5(sin(2t)+2tcos(2t))

What is the first derivative of f(t)=e^{5tsin(2t)} ?

The first derivative of f(t)=e^{5tsin(2t)} is e^{5tsin(2t)}*5(sin(2t)+2tcos(2t))

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derivative of

f (t) = e^{5 t s i n (2 t)}

e^{5 t s i n (2 t)} \cdot 5 (sin (2 t) + 2 t cos (2 t))

Solution steps

\frac{d}{d t} (e^{5 t s i n (2 t)})

Apply the chain rule:

e^{5 t s i n (2 t)} \frac{d}{d t} (5 t sin (2 t))

= e^{5 t s i n (2 t)} \frac{d}{d t} (5 t sin (2 t))

\frac{d}{d t} (5 t sin (2 t)) = 5 (sin (2 t) + 2 t cos (2 t))

= e^{5 t s i n (2 t)} \cdot 5 (sin (2 t) + 2 t cos (2 t))

What is the derivative of f(t)=e^{5tsin(2t)} ?
The derivative of f(t)=e^{5tsin(2t)} is e^{5tsin(2t)}*5(sin(2t)+2tcos(2t))
What is the first derivative of f(t)=e^{5tsin(2t)} ?
The first derivative of f(t)=e^{5tsin(2t)} is e^{5tsin(2t)}*5(sin(2t)+2tcos(2t))