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Popular >

derivative of f(t)=e^{3tsin(2t)}

Solution

derivative of

f (t) = e^{3 t s i n (2 t)}

Solution

e^{3 t s i n (2 t)} \cdot 3 (sin (2 t) + 2 t cos (2 t))

Solution steps

\frac{d}{d t} (e^{3 t s i n (2 t)})

Apply the chain rule:

e^{3 t s i n (2 t)} \frac{d}{d t} (3 t sin (2 t))

= e^{3 t s i n (2 t)} \frac{d}{d t} (3 t sin (2 t))

\frac{d}{d t} (3 t sin (2 t)) = 3 (sin (2 t) + 2 t cos (2 t))

= e^{3 t s i n (2 t)} \cdot 3 (sin (2 t) + 2 t cos (2 t))

Popular Examples

derivative of (ln|x|^e+x/(11))

\frac{d}{d x} ((ln ∣ x ∣)^{e} + \frac{x}{11})

25y^{''}-10y^'+y=0

25 y^{^{''}} - 10 y^{^{'}} + y = 0

derivative of log_{3}(2x+5)derivative of

lo g_{3} (2 x + 5)

integral of (sec^2(t))/(1+tan(t))

\int \frac{sec ^{2} ( t )}{1 + tan ( t )} d t

integral of ((2y^{1/2})/(y^3))0x

\int (\frac{2 y ^{\frac{1}{2}}}{y ^{3}}) d^{0} x

Frequently Asked Questions (FAQ)

What is the derivative of f(t)=e^{3tsin(2t)} ?
The derivative of f(t)=e^{3tsin(2t)} is e^{3tsin(2t)}*3(sin(2t)+2tcos(2t))
What is the first derivative of f(t)=e^{3tsin(2t)} ?
The first derivative of f(t)=e^{3tsin(2t)} is e^{3tsin(2t)}*3(sin(2t)+2tcos(2t))