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Popular >

derivative of f(t)=e^{4tsin(2t)}

Solution

derivative of

f (t) = e^{4 t s i n (2 t)}

Solution

e^{4 t s i n (2 t)} \cdot 4 (sin (2 t) + 2 t cos (2 t))

Solution steps

\frac{d}{d t} (e^{4 t s i n (2 t)})

Apply the chain rule:

e^{4 t s i n (2 t)} \frac{d}{d t} (4 t sin (2 t))

= e^{4 t s i n (2 t)} \frac{d}{d t} (4 t sin (2 t))

\frac{d}{d t} (4 t sin (2 t)) = 4 (sin (2 t) + 2 t cos (2 t))

= e^{4 t s i n (2 t)} \cdot 4 (sin (2 t) + 2 t cos (2 t))

Popular Examples

integral of (sin(2x))/(x^2)

\int \frac{sin ( 2 x )}{x ^{2}} d x

integral of x^3ln(6x)

\int x^{3} ln (6 x) d x

derivative of sqrt(x)cos(sqrt(x))

\frac{d}{d x} (x cos (x))

integral of (y-1)/(y+4)

\int \frac{y - 1}{y + 4} d y

limit as x approaches 3 of 6x^2

x \to 3 lim (6 x^{2})

Frequently Asked Questions (FAQ)

What is the derivative of f(t)=e^{4tsin(2t)} ?
The derivative of f(t)=e^{4tsin(2t)} is e^{4tsin(2t)}*4(sin(2t)+2tcos(2t))
What is the first derivative of f(t)=e^{4tsin(2t)} ?
The first derivative of f(t)=e^{4tsin(2t)} is e^{4tsin(2t)}*4(sin(2t)+2tcos(2t))