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Popular >

derivative of e^{6tsin(2t)}

Solution

derivative of

e^{6 t s i n (2 t)}

Solution

e^{6 t s i n (2 t)} \cdot 6 (sin (2 t) + 2 t cos (2 t))

Solution steps

\frac{d}{d t} (e^{6 t s i n (2 t)})

Apply the chain rule:

e^{6 t s i n (2 t)} \frac{d}{d t} (6 t sin (2 t))

= e^{6 t s i n (2 t)} \frac{d}{d t} (6 t sin (2 t))

\frac{d}{d t} (6 t sin (2 t)) = 6 (sin (2 t) + 2 t cos (2 t))

= e^{6 t s i n (2 t)} \cdot 6 (sin (2 t) + 2 t cos (2 t))

Popular Examples

derivative of e^{3x+2}

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

integral of (5x^2-10x-8)/(x^3-4x)

\int \frac{5 x ^{2} - 10 x - 8}{x ^{3} - 4 x} d x

integral of 3/((t^2+1)^{3/2)}

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

(x^2+1)(dy)/(dx)+3x(y-1)=0,y(0)=4

(x^{2} + 1) \frac{d y}{d x} + 3 x (y - 1) = 0, y (0) = 4

(\partial)/(\partial x)(xcos(yln(x)))

\frac{\partial}{\partial x} (x cos (y ln (x)))

Frequently Asked Questions (FAQ)

What is the derivative of e^{6tsin(2t)} ?
The derivative of e^{6tsin(2t)} is e^{6tsin(2t)}*6(sin(2t)+2tcos(2t))
What is the first derivative of e^{6tsin(2t)} ?
The first derivative of e^{6tsin(2t)} is e^{6tsin(2t)}*6(sin(2t)+2tcos(2t))